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Volumn 45, Issue 4, 2008, Pages 535-593

Variational methods in relativistic quantum mechanics

Author keywords

Critical points; Dirac operator; Dirac Fock equations; Ground state; Mean field approximation; Non relativistic limit; Nonlinear eigenvalue problems; Quantum chemistry; Relativistic quantum mechanics; Strongly indefinite functionals; Variational methods

Indexed keywords


EID: 55849138398     PISSN: 02730979     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0273-0979-08-01212-3     Document Type: Review
Times cited : (120)

References (174)
  • 1
    • 55849084218 scopus 로고    scopus 로고
    • S. Abenda. Solitary waves for Maxwell-Dirac and Coulomb-Dirac models. Ann. Inst. H. Poincaré, Phys. Théor. 88(2) (1998). 229-244. MR1618672 (99c:81023)
    • S. Abenda. Solitary waves for Maxwell-Dirac and Coulomb-Dirac models. Ann. Inst. H. Poincaré, Phys. Théor. 88(2) (1998). 229-244. MR1618672 (99c:81023)
  • 2
    • 0001563645 scopus 로고
    • Saddle points and multiple solutions of differential equations
    • MR550724 80j:47078
    • H. Amann. Saddle points and multiple solutions of differential equations. Math. Z. 169 (1979), 127-166. MR550724 (80j:47078)
    • (1979) Math. Z , vol.169 , pp. 127-166
    • Amann, H.1
  • 3
    • 36149018028 scopus 로고
    • The Positive Electron
    • C.D. Anderson. The Positive Electron. Phys. Rev. 43 (1933), 491-494.
    • (1933) Phys. Rev , vol.43 , pp. 491-494
    • Anderson, C.D.1
  • 4
    • 12444276762 scopus 로고    scopus 로고
    • W.H. Aschbacher. Lowering the Hartree-Fock minimizer by electron-positron pair correlation. Lett. Math. Phys. 70(1), (2004), 29-41. MR2107703 (2006b:81064)
    • W.H. Aschbacher. Lowering the Hartree-Fock minimizer by electron-positron pair correlation. Lett. Math. Phys. 70(1), (2004), 29-41. MR2107703 (2006b:81064)
  • 5
    • 55849116637 scopus 로고    scopus 로고
    • V. Bach, J.M. Barbaroux, B. Helfer, H. Siedentop. Stability of matter for the HartrecFock functional of the relativistic electron-positron field. Doc. Math. 3 (1998), 353-364. MR1668924 (2001a:81082)
    • V. Bach, J.M. Barbaroux, B. Helfer, H. Siedentop. Stability of matter for the HartrecFock functional of the relativistic electron-positron field. Doc. Math. 3 (1998), 353-364. MR1668924 (2001a:81082)
  • 6
    • 0033246643 scopus 로고    scopus 로고
    • V. Bach, J.M. Barbaroux, B. Helffer, H. Siedentop. On the stability of the relativistic electron-positron field. Comm. Math. Phys. 201(2) (1999), 445-460. MR1682210 (2000i:81169)
    • V. Bach, J.M. Barbaroux, B. Helffer, H. Siedentop. On the stability of the relativistic electron-positron field. Comm. Math. Phys. 201(2) (1999), 445-460. MR1682210 (2000i:81169)
  • 7
    • 0000203351 scopus 로고
    • There are no unfilled shells in unrestricted Hartree-Fock theory
    • V. Bach, E.H. Lieb, M. Loss, J.P. Solovej. There are no unfilled shells in unrestricted Hartree-Fock theory. Phys. Rev. Lett. 72(19) (1994), 2981-2983.
    • (1994) Phys. Rev. Lett , vol.72 , Issue.19 , pp. 2981-2983
    • Bach, V.1    Lieb, E.H.2    Loss, M.3    Solovej, J.P.4
  • 8
    • 0009000148 scopus 로고
    • Problème de Cauchy global pour des systèmes de Dirac-Klein-Gordon.
    • MR969173 90i:81024
    • A. Bachelot. Problème de Cauchy global pour des systèmes de Dirac-Klein-Gordon. Ann. Inst. H. Poincaré 48 (1988), 387-422. MR969173 (90i:81024)
    • (1988) Ann. Inst. H. Poincaré , vol.48 , pp. 387-422
    • Bachelot, A.1
  • 9
    • 0032380199 scopus 로고    scopus 로고
    • Nonlinear Dirac Helds on the Schwarzschild metric
    • MR1633146 99e:83010
    • A. Bachelot-Motet. Nonlinear Dirac Helds on the Schwarzschild metric. Classical Quantum. Gravity 15 (1998), 1815-1825. MR1633146 (99e:83010)
    • (1998) Classical Quantum. Gravity , vol.15 , pp. 1815-1825
    • Bachelot-Motet, A.1
  • 10
    • 84990623267 scopus 로고
    • On a nonlinear elliptic equation involving the critical Sobolev exponent: The effect of the topology of the domain
    • MR929280 89c:35053
    • A. Bahri, J.-M. Coron. On a nonlinear elliptic equation involving the critical Sobolev exponent: the effect of the topology of the domain. Comm. Pure Appl. Math. 41(3) (1988), 253-294. MR929280 (89c:35053)
    • (1988) Comm. Pure Appl. Math , vol.41 , Issue.3 , pp. 253-294
    • Bahri, A.1    Coron, J.-M.2
  • 11
    • 0000666059 scopus 로고
    • Existence of excited states for a nonlinear Dirac field
    • MR968485 90b:35195
    • M. Balabane, T. Cazenave, A. Douady, F. Merle. Existence of excited states for a nonlinear Dirac field. Comm. Math. Phys. 119 (1988). 153-176. MR968485 (90b:35195)
    • (1988) Comm. Math. Phys , vol.119 , pp. 153-176
    • Balabane, M.1    Cazenave, T.2    Douady, A.3    Merle, F.4
  • 12
    • 0001893375 scopus 로고
    • Existence of standing waves for Dirac fields with singular nonlinearities
    • MR1071235 91k:81025
    • M. Balabane, T. Cazenave, L. Vazquez. Existence of standing waves for Dirac fields with singular nonlinearities. Comm. Math. Phys. 133 (1990), 53-74. MR1071235 (91k:81025)
    • (1990) Comm. Math. Phys , vol.133 , pp. 53-74
    • Balabane, M.1    Cazenave, T.2    Vazquez, L.3
  • 13
    • 15244360825 scopus 로고    scopus 로고
    • J.-M. Barbaroux, M. J. Esteban, E. Séré. Some connections between Dirac-Fock and electron-positron Hartree-Fock. Ann. Henri Poincaré 6(1) (2005), 85-102. MR2119356 (2006b:81065)
    • J.-M. Barbaroux, M. J. Esteban, E. Séré. Some connections between Dirac-Fock and electron-positron Hartree-Fock. Ann. Henri Poincaré 6(1) (2005), 85-102. MR2119356 (2006b:81065)
  • 14
    • 21244439209 scopus 로고    scopus 로고
    • J.-M. Barbaroux, W. Farkas, B. Helfer, H. Siedentop. On the Hartree-Fock Equations of the Electron-Positron Field. Comm. Math. Phys. 255 (2005), 131-159. MR2123379 (2006c:81227)
    • J.-M. Barbaroux, W. Farkas, B. Helfer, H. Siedentop. On the Hartree-Fock Equations of the Electron-Positron Field. Comm. Math. Phys. 255 (2005), 131-159. MR2123379 (2006c:81227)
  • 15
    • 29144498971 scopus 로고    scopus 로고
    • J.-M. Barbaroux, B. Helfer, H. Siedentop. Remarks on the Mittleman max-min variational method for the electron-positron field. J. Phys. A 39(1) (2006), 85-98. MR2200186 (2007d:81060)
    • J.-M. Barbaroux, B. Helfer, H. Siedentop. Remarks on the Mittleman max-min variational method for the electron-positron field. J. Phys. A 39(1) (2006), 85-98. MR2200186 (2007d:81060)
  • 16
    • 0008731976 scopus 로고
    • Stable variational calculations with the Dirac Hamiltonian
    • W.E. Bayliss, S. J. Peel. Stable variational calculations with the Dirac Hamiltonian. Phys. Rev. A. 28(4) (1983), 2552-2554.
    • (1983) Phys. Rev. A , vol.28 , Issue.4 , pp. 2552-2554
    • Bayliss, W.E.1    Peel, S.J.2
  • 17
    • 1542437218 scopus 로고
    • Critical point theorems for indefinite functionals
    • MR537061 80i:58019
    • V. Bend, P.H. Rabinowitz. Critical point theorems for indefinite functionals. Inv. Math. 52 (1979), 336-352. MR537061 (80i:58019)
    • (1979) Inv. Math , vol.52 , pp. 336-352
    • Bend, V.1    Rabinowitz, P.H.2
  • 18
    • 55849145785 scopus 로고    scopus 로고
    • A. Berthier, V. Georgescu. Sur le spectre ponctuel de l'opérateur de Dirac. C. R. Acad. Sci. Paris. Sér. A 297 (1983), p. 335-338. MR732500 (86f:35137)
    • A. Berthier, V. Georgescu. Sur le spectre ponctuel de l'opérateur de Dirac. C. R. Acad. Sci. Paris. Sér. A 297 (1983), p. 335-338. MR732500 (86f:35137)
  • 19
    • 0008732773 scopus 로고
    • On the point spectrum for Dirac operators
    • MR880983 89b:35131
    • A. Berthier, V. Georgescu. On the point spectrum for Dirac operators. J. Funct. Anal. 71 (1987), 309-338. MR880983 (89b:35131)
    • (1987) J. Funct. Anal , vol.71 , pp. 309-338
    • Berthier, A.1    Georgescu, V.2
  • 21
    • 33750380381 scopus 로고    scopus 로고
    • Stable directions for small nonlinear Dirac standing waves
    • MR2259214
    • N. Boussaid. Stable directions for small nonlinear Dirac standing waves. Comm. Math. Phys. 288(3) (2006), 757-817. MR2259214
    • (2006) Comm. Math. Phys , vol.288 , Issue.3 , pp. 757-817
    • Boussaid, N.1
  • 22
    • 0000183710 scopus 로고    scopus 로고
    • Local existence for the Maxwell-Dirac equations in three space dimensions
    • MR1391520 97f:35176
    • N. Bournaveas. Local existence for the Maxwell-Dirac equations in three space dimensions. Comm. Partial Differential Equations 21(5-6) (1996), 693-720. MR1391520 (97f:35176)
    • (1996) Comm. Partial Differential Equations , vol.21 , Issue.5-6 , pp. 693-720
    • Bournaveas, N.1
  • 23
    • 0033451332 scopus 로고    scopus 로고
    • N. Bournaveas. Local existence of energy class solutions for the Dirac-Klein-Gordon equations. Comm. Partial Differential Equations 24(7-8) (1999), 1167-1193. MR1697486 (2000e:35188)
    • N. Bournaveas. Local existence of energy class solutions for the Dirac-Klein-Gordon equations. Comm. Partial Differential Equations 24(7-8) (1999), 1167-1193. MR1697486 (2000e:35188)
  • 24
    • 55849142859 scopus 로고    scopus 로고
    • H. Booth. Electrons with self-field as solutions to nonlinear PDE. Geometric analysis and applications (Canberra, 2000), 1-14. Proc. Centre Math. Appl. Austral. Nat. Univ., 39, Austral. Nat. Univ., Canberra. 2001. MR1852690 (2002h:81104)
    • H. Booth. Electrons with self-field as solutions to nonlinear PDE. Geometric analysis and applications (Canberra, 2000), 1-14. Proc. Centre Math. Appl. Austral. Nat. Univ., 39, Austral. Nat. Univ., Canberra. 2001. MR1852690 (2002h:81104)
  • 25
    • 84990613834 scopus 로고
    • Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents
    • MR709644 84h:35059
    • H. Brézis, L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical Sobolev exponents. Comm. Pure Appl. Math. 36(4) (1983), 437-477. MR709644 (84h:35059)
    • (1983) Comm. Pure Appl. Math , vol.36 , Issue.4 , pp. 437-477
    • Brézis, H.1    Nirenberg, L.2
  • 26
    • 33744545310 scopus 로고    scopus 로고
    • B. Buffoni, M.J. Esteban, E. Séré. Normalized solutions to strongly indefinite semilinear equations. Adv. Nonlinear Stud. 6(2) (2006), 323-347. MR2219842 (2007e:35072)
    • B. Buffoni, M.J. Esteban, E. Séré. Normalized solutions to strongly indefinite semilinear equations. Adv. Nonlinear Stud. 6(2) (2006), 323-347. MR2219842 (2007e:35072)
  • 27
    • 85011586206 scopus 로고
    • Minimax characterization of solutions for a semi-linear elliptic equation with lack of compactness
    • MR1246458 94m:35099
    • B. Buffoni, L. Jeanjean. Minimax characterization of solutions for a semi-linear elliptic equation with lack of compactness. Ann. Inst. H. Poincaré Anal. Non Linéare 10(4) (1993), 377-404. MR1246458 (94m:35099)
    • (1993) Ann. Inst. H. Poincaré Anal. Non Linéare , vol.10 , Issue.4 , pp. 377-404
    • Buffoni, B.1    Jeanjean, L.2
  • 28
    • 84966228956 scopus 로고
    • Existence of a nontrivial solution to a strongly indefinite semilinear equation
    • MR1145940 93k:35086
    • B. Buffoni, L. Jeanjean, C. A. Stuart. Existence of a nontrivial solution to a strongly indefinite semilinear equation. Proc. Amer. Math. Soc. 119(1) (1993), 179-186 MR1145940 (93k:35086)
    • (1993) Proc. Amer. Math. Soc , vol.119 , Issue.1 , pp. 179-186
    • Buffoni, B.1    Jeanjean, L.2    Stuart, C.A.3
  • 29
    • 22444453061 scopus 로고    scopus 로고
    • On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms
    • MR1642120 99i:47091
    • V.I. Burenkov, N.D. Evans. On the evaluation of the norm of an integral operator associated with the stability of one-electron atoms. Proc. Roy. Soc. Edinburgh, Sect. A 128(5) (1998), 993-1005. MR1642120 (99i:47091)
    • (1998) Proc. Roy. Soc. Edinburgh, Sect. A , vol.128 , Issue.5 , pp. 993-1005
    • Burenkov, V.I.1    Evans, N.D.2
  • 30
    • 44349084730 scopus 로고    scopus 로고
    • A new approach to the modelling of local defects in crystals: The reduced Hartree-Fock case
    • É. Cancès, A. Deleurence, M. Lewin. A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case. Comm. Math. Phys., 281 (2008), 129-177.
    • (2008) Comm. Math. Phys , vol.281 , pp. 129-177
    • Cancès, E.1    Deleurence, A.2    Lewin, M.3
  • 31
    • 0000197934 scopus 로고
    • Applications of a min-max principle
    • MR0501089 58:18544
    • A. Castro, A.C. Lazer. Applications of a min-max principle. Rev. Colombiana Mat. 10 (1976), 141-149. MR0501089 (58:18544)
    • (1976) Rev. Colombiana Mat , vol.10 , pp. 141-149
    • Castro, A.1    Lazer, A.C.2
  • 32
    • 3042893126 scopus 로고
    • On the existence of stationary states for classical nonlinear Dirac fields
    • CMAF, Lisbonne
    • T. Cazenave. On the existence of stationary states for classical nonlinear Dirac fields. In Hyperbolic systems and Mathematical Physics. Textos e Notas 4, CMAF, Lisbonne (1989).
    • (1989) Hyperbolic systems and Mathematical Physics. Textos e Notas , vol.4
    • Cazenave, T.1
  • 33
    • 0002412216 scopus 로고
    • Existence of localized solutions for a classical nonlinear Dirac field
    • MR847126 87j:81027
    • T. Cazenave, L. Vazquez. Existence of localized solutions for a classical nonlinear Dirac field, Comm. Math. Phys. 105 (1986), 35-47. MR847126 (87j:81027)
    • (1986) Comm. Math. Phys , vol.105 , pp. 35-47
    • Cazenave, T.1    Vazquez, L.2
  • 34
    • 0001158606 scopus 로고
    • Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac system in one space dimension
    • NIR0368640 51:4881
    • J. Chadam. Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac system in one space dimension. J. Funct. Anal. 13 (1973), 173-184. NIR0368640 (51:4881)
    • (1973) J. Funct. Anal , vol.13 , pp. 173-184
    • Chadam, J.1
  • 35
    • 0016928469 scopus 로고
    • On the Maxwell-Dirac equations with zero magnetic field and their solutions in two space dimensions
    • MR0413833 54:1947
    • J. Chadam, R. Glassey. On the Maxwell-Dirac equations with zero magnetic field and their solutions in two space dimensions. J. Math. Anal. Appl. 53 (1976), 495-507. MR0413833 (54:1947)
    • (1976) J. Math. Anal. Appl , vol.53 , pp. 495-507
    • Chadam, J.1    Glassey, R.2
  • 36
    • 0000865554 scopus 로고    scopus 로고
    • P. Chaix, D. Iracane. The Bogoliubov-Dirac-Fock formalism. I. J. Phys. At. Mol. Opt. Phys. 22 (1989), 3791-3814.
    • P. Chaix, D. Iracane. The Bogoliubov-Dirac-Fock formalism. I. J. Phys. At. Mol. Opt. Phys. 22 (1989), 3791-3814.
  • 38
    • 0000051530 scopus 로고
    • Solutions globales des équations de Maxwell-Dirac-Klein-Gordon (masses nulles).
    • MR610307 82f:81037
    • Y. Choquet-Bruhat. Solutions globales des équations de Maxwell-Dirac-Klein-Gordon (masses nulles). C. R. Acad. Sci. Paris, Série I 292 (1981), 153-158. MR610307 (82f:81037)
    • (1981) C. R. Acad. Sci. Paris, Série I , vol.292 , pp. 153-158
    • Choquet-Bruhat, Y.1
  • 39
    • 84980158831 scopus 로고
    • Hamiltonian trajectories having prescribed minimal period
    • MR562546 81e:70017
    • F.H. Clarke, I. Ekeland. Hamiltonian trajectories having prescribed minimal period. Comm. Pure Appl. Math. 33(2) (1980), 103-116. MR562546 (81e:70017)
    • (1980) Comm. Pure Appl. Math , vol.33 , Issue.2 , pp. 103-116
    • Clarke, F.H.1    Ekeland, I.2
  • 40
    • 0015249887 scopus 로고
    • 3 = 0 and a variational characterization of other solutions
    • MR0333489 48:11814
    • 3 = 0 and a variational characterization of other solutions. Arch. Rat. Mech. Anal. 46 (1972), 81-95. MR0333489 (48:11814)
    • (1972) Arch. Rat. Mech. Anal , vol.46 , pp. 81-95
    • Coffman, C.V.1
  • 41
    • 0002741292 scopus 로고    scopus 로고
    • C. Conley, E. Zehnder. The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold, Invent. Math. 73 (1983), 33-49. MR707347 (85e:58044)
    • C. Conley, E. Zehnder. The Birkhoff-Lewis fixed point theorem and a conjecture of V.I. Arnold, Invent. Math. 73 (1983), 33-49. MR707347 (85e:58044)
  • 42
    • 0008716679 scopus 로고
    • The minimax technique in relativistic Hartree-Fock calculations
    • S.N. Datta, G. Deviah. The minimax technique in relativistic Hartree-Fock calculations, Pramana 30(5) (1988), 393-416.
    • (1988) Pramana , vol.30 , Issue.5 , pp. 393-416
    • Datta, S.N.1    Deviah, G.2
  • 43
    • 55849098490 scopus 로고    scopus 로고
    • s for the massive nonlinear Dirac equations in three space dimensions. Boll. Unione Mat. Ital. B (7) 1(3) (1987), 861-874. MR916298 (89f:35181)
    • s for the massive nonlinear Dirac equations in three space dimensions. Boll. Unione Mat. Ital. B (7) 1(3) (1987), 861-874. MR916298 (89f:35181)
  • 44
    • 0000154144 scopus 로고
    • The quantum theory of the electron
    • P.A.M. Dirac. The quantum theory of the electron. Proc. Roy. Soc. A 117 (1928), 610-624.
    • (1928) Proc. Roy. Soc. A , vol.117 , pp. 610-624
    • Dirac, P.A.M.1
  • 45
    • 0001293350 scopus 로고
    • A theory of electrons and protons
    • P.A.M. Dirac. A theory of electrons and protons. Proc. Roy. Soc. A 128 (1930), 360-365.
    • (1930) Proc. Roy. Soc. A , vol.128 , pp. 360-365
    • Dirac, P.A.M.1
  • 46
    • 55849108047 scopus 로고    scopus 로고
    • P.A.M. Dirac. Théorie du positron. Solvay report (1934). 203-212. Gauthier-Villars, Paris. XXV, 353 S.
    • P.A.M. Dirac. Théorie du positron. Solvay report (1934). 203-212. Gauthier-Villars, Paris. XXV, 353 S.
  • 47
    • 34548776972 scopus 로고
    • Discussion of the infinite distribution of electrons in the theory of the positron
    • P.A.M. Dirac. Discussion of the infinite distribution of electrons in the theory of the positron. Proc. Camb. Philos. Soc. 30 (1934), 150-163.
    • (1934) Proc. Camb. Philos. Soc , vol.30 , pp. 150-163
    • Dirac, P.A.M.1
  • 48
    • 34547726624 scopus 로고    scopus 로고
    • Relativistic hydrogenic atoms in strong magnetic fields
    • MR2333781
    • J. Dolbcault, M.J. Esteban, M. Loss. Relativistic hydrogenic atoms in strong magnetic fields. Ann. Henri Poincaré 8(4) (2007), 749-779. MR2333781
    • (2007) Ann. Henri Poincaré , vol.8 , Issue.4 , pp. 749-779
    • Dolbcault, J.1    Esteban, M.J.2    Loss, M.3
  • 49
    • 4344635402 scopus 로고    scopus 로고
    • J. Dolbeault, M.J. Esteban, M. Loss, L. Vega. An analytical proof of Hardy-like inequalities related to the Dirac operator. J. Funct. Anal. 218 (2004), 1-21. MR2091354 (2005h:35291)
    • J. Dolbeault, M.J. Esteban, M. Loss, L. Vega. An analytical proof of Hardy-like inequalities related to the Dirac operator. J. Funct. Anal. 218 (2004), 1-21. MR2091354 (2005h:35291)
  • 50
    • 0007320123 scopus 로고    scopus 로고
    • J. Dolbeault, M.J. Esteban, E. Séré. Variational characterization for eigenvalues of Dirac operators. Calc. Var. Partial Differential Equations 10 (2000), 321-347. MR1767717 (2001f:49083)
    • J. Dolbeault, M.J. Esteban, E. Séré. Variational characterization for eigenvalues of Dirac operators. Calc. Var. Partial Differential Equations 10 (2000), 321-347. MR1767717 (2001f:49083)
  • 51
    • 0013373561 scopus 로고    scopus 로고
    • J. Dolbeault, M.J. Esteban, E. Séré. On the eigenvalues of operators with gaps. Application to Dirac operators. J. Funct. Anal. 174 (2000), 208-226. MR1761368 (2001e:47040)
    • J. Dolbeault, M.J. Esteban, E. Séré. On the eigenvalues of operators with gaps. Application to Dirac operators. J. Funct. Anal. 174 (2000), 208-226. MR1761368 (2001e:47040)
  • 52
    • 0038731130 scopus 로고    scopus 로고
    • A variational method for relativistic computations in atomic and molecular physics
    • J. Dolbeault, M.J. Esteban, E. Séré. A variational method for relativistic computations in atomic and molecular physics. Int. J. Quantum Chemistry 93 (2003), 149-155.
    • (2003) Int. J. Quantum Chemistry , vol.93 , pp. 149-155
    • Dolbeault, J.1    Esteban, M.J.2    Séré, E.3
  • 53
    • 33745657456 scopus 로고    scopus 로고
    • J. Dolbeault, M. J. Esteban, E. Séré. General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators. J. Eur. Math. Soc. 8(2) (2006), 243-251. MR2239275 (2007m:47044)
    • J. Dolbeault, M. J. Esteban, E. Séré. General results on the eigenvalues of operators with gaps, arising from both ends of the gaps. Application to Dirac operators. J. Eur. Math. Soc. 8(2) (2006), 243-251. MR2239275 (2007m:47044)
  • 54
    • 14344272345 scopus 로고    scopus 로고
    • Minimization methods for the one-particle Dirac equation
    • J. Dolbeault, M.J. Esteban, E. Séré, M. Vanbreugel. Minimization methods for the one-particle Dirac equation. Phys. Rev. Lett. 85(19) (2000), 4020-4023.
    • (2000) Phys. Rev. Lett , vol.85 , Issue.19 , pp. 4020-4023
    • Dolbeault, J.1    Esteban, M.J.2    Séré, E.3    Vanbreugel, M.4
  • 55
    • 4243078423 scopus 로고
    • Application of discrete-basis-set methods to the Dirac equation
    • G.W.F. Drake, S.P. Goldman. Application of discrete-basis-set methods to the Dirac equation. Phys. Rev. A 23 (1981), 2093-2098.
    • (1981) Phys. Rev. A , vol.23 , pp. 2093-2098
    • Drake, G.W.F.1    Goldman, S.P.2
  • 56
    • 0347364147 scopus 로고
    • Relativistic Sturmian and finite basis set methods in atomic physics
    • G.W.F. Drake, S.P. Goldman. Relativistic Sturmian and finite basis set methods in atomic physics. Adv. Atomic Molecular Phys. 23 (1988), 23-29.
    • (1988) Adv. Atomic Molecular Phys , vol.23 , pp. 23-29
    • Drake, G.W.F.1    Goldman, S.P.2
  • 58
    • 55849131731 scopus 로고    scopus 로고
    • Ph. Durand. Transformation du Hamiltonian de Dirac en Hamiltoniens variationnels de type Pauli. Application à des atomes hydrogenoïdes. C. R. Acad. Sci. Paris 303(2) (1986), 119-124.
    • Ph. Durand. Transformation du Hamiltonian de Dirac en Hamiltoniens variationnels de type Pauli. Application à des atomes hydrogenoïdes. C. R. Acad. Sci. Paris 303(2) (1986), 119-124.
  • 59
    • 0000815311 scopus 로고
    • Effective Hamiltonians and pseudo-potentials as tools for rigorous modelling
    • K.P. Lawley ed, J. Wiley & Sons
    • Ph. Durand, J.-P. Malrieu. Effective Hamiltonians and pseudo-potentials as tools for rigorous modelling. In Ab initio methods in Quantum Chemistry I. K.P. Lawley ed., J. Wiley & Sons, 1987.
    • (1987) Ab initio methods in Quantum Chemistry I
    • Durand, P.1    Malrieu, J.-P.2
  • 60
    • 0031528934 scopus 로고    scopus 로고
    • 3) for s > 1
    • MR1434039 97k:35239
    • 3) for s > 1. SIAM J. Math. Anal. 28(2) (1997), 338-362. MR1434039 (97k:35239)
    • (1997) SIAM J. Math. Anal , vol.28 , Issue.2 , pp. 338-362
    • Escobedo, M.1    Vega, L.2
  • 61
    • 3042986444 scopus 로고    scopus 로고
    • Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations
    • MR1386737 97g:35144
    • M.J. Esteban, V. Georgiev, E. Séré. Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations. Cal. Var. Partial Differential Equations 4 (1996), 265-281. MR1386737 (97g:35144)
    • (1996) Cal. Var. Partial Differential Equations , vol.4 , pp. 265-281
    • Esteban, M.J.1    Georgiev, V.2    Séré, E.3
  • 62
    • 0039088429 scopus 로고
    • Stationary states of the nonlinear Dirac equation: A variational approach
    • MR1344729 96g:81041
    • M.J. Esteban, E. Séré. Stationary states of the nonlinear Dirac equation: a variational approach. Comm. Math. Phys. 171 (1995), 323-350. MR1344729 (96g:81041)
    • (1995) Comm. Math. Phys , vol.171 , pp. 323-350
    • Esteban, M.J.1    Séré, E.2
  • 63
    • 0009019766 scopus 로고    scopus 로고
    • Existence and multiplicity of solutions for linear and nonlinear Dirac problems
    • Partial Differential Equations and Their Applications, Eds. P.C. Greiner, V. Ivrii, L.A. Seco and C. Sulam, AMS
    • M.J. Esteban, E. Séré. Existence and multiplicity of solutions for linear and nonlinear Dirac problems. Partial Differential Equations and Their Applications. CRM Proceedings and Lecture Notes. vol. 12, Eds. P.C. Greiner, V. Ivrii, L.A. Seco and C. Sulam, AMS, 1997.
    • (1997) CRM Proceedings and Lecture Notes , vol.12
    • Esteban, M.J.1    Séré, E.2
  • 64
    • 0033242952 scopus 로고    scopus 로고
    • M.J. Esteban, E. Séré. Solutions for the Dirac-Fock equations for atoms and molecules. Comm. Math. Phys. 203 (1999), 499-530. MR1700174 (2000j:81057)
    • M.J. Esteban, E. Séré. Solutions for the Dirac-Fock equations for atoms and molecules. Comm. Math. Phys. 203 (1999), 499-530. MR1700174 (2000j:81057)
  • 65
    • 0035540791 scopus 로고    scopus 로고
    • M.J. Esteban. E. Séré. Nonrelativistic limit of the Dirac-Fock equations. Ann. Henri Poincaré 2 (2001), 941-961. MR 1869528 (2003d:81066)
    • M.J. Esteban. E. Séré. Nonrelativistic limit of the Dirac-Fock equations. Ann. Henri Poincaré 2 (2001), 941-961. MR 1869528 (2003d:81066)
  • 66
    • 55849100300 scopus 로고    scopus 로고
    • M.J. Esteban, E. Séré. A max-min principle for the ground state of the Dirac-Fock functional. Contemp. Math. 307 (2002), 135-141. MR1946024 (2003k:81052)
    • M.J. Esteban, E. Séré. A max-min principle for the ground state of the Dirac-Fock functional. Contemp. Math. 307 (2002), 135-141. MR1946024 (2003k:81052)
  • 67
    • 0030558277 scopus 로고    scopus 로고
    • The spectrum of relativistic one-electron atoms according to Bethe and Salpeter
    • MR1395212 97e:81019
    • W.D. Evans, P. Perry, H. Siedentop. The spectrum of relativistic one-electron atoms according to Bethe and Salpeter. Comm. Math. Phys. 178 (1996). 733-746. MR1395212 (97e:81019)
    • (1996) Comm. Math. Phys , vol.178 , pp. 733-746
    • Evans, W.D.1    Perry, P.2    Siedentop, H.3
  • 68
    • 0000388157 scopus 로고
    • Morse-type information on Palais-Smale sequences obtained by min-max principles
    • MR1303222 95m:58028
    • G. Fang, N. Ghoussoub. Morse-type information on Palais-Smale sequences obtained by min-max principles. Comm. Pure Appl. Math. 47(12) (1994). 1595-1653. MR1303222 (95m:58028)
    • (1994) Comm. Pure Appl. Math , vol.47 , Issue.12 , pp. 1595-1653
    • Fang, G.1    Ghoussoub, N.2
  • 69
    • 36149014299 scopus 로고
    • Nonlinear spinor fields
    • MR0042204 13:76b
    • R. Finkelstein, R. Lelevier, M. Ruderman. Nonlinear spinor fields. Phys. Rev. 83 (1951), 326-332. MR0042204 (13:76b)
    • (1951) Phys. Rev , vol.83 , pp. 326-332
    • Finkelstein, R.1    Lelevier, R.2    Ruderman, M.3
  • 71
    • 0001417829 scopus 로고    scopus 로고
    • F. Finster, J. Smoller, S.-T. Yau. Particle-like solutions of the Einstein-Dirac-Maxwell equations. Phys. Lett. A. 259(6) (1999), 431-436. MR1714646 (2000f:83016)
    • F. Finster, J. Smoller, S.-T. Yau. Particle-like solutions of the Einstein-Dirac-Maxwell equations. Phys. Lett. A. 259(6) (1999), 431-436. MR1714646 (2000f:83016)
  • 72
    • 0033245035 scopus 로고    scopus 로고
    • F. Finster, J. Smoller, S.-T. Yau. Non-existence of black hole solutions for a spherically symmetric, static Einstein-Dirac-Maxwell system. Comm. Math. Phys. 205(2) (1999), 249-262. MR1712611 (2000k:83008)
    • F. Finster, J. Smoller, S.-T. Yau. Non-existence of black hole solutions for a spherically symmetric, static Einstein-Dirac-Maxwell system. Comm. Math. Phys. 205(2) (1999), 249-262. MR1712611 (2000k:83008)
  • 73
    • 0011036978 scopus 로고
    • On the global solutions of the Maxwell-Dirac equations
    • MR904136 88k:35117
    • M. Flato, J. Simon, E. Taflin. On the global solutions of the Maxwell-Dirac equations. Comm. Math. Phys. 113 (1987), 21-49. MR904136 (88k:35117)
    • (1987) Comm. Math. Phys , vol.113 , pp. 21-49
    • Flato, M.1    Simon, J.2    Taflin, E.3
  • 74
    • 84968501737 scopus 로고
    • Morse theory for fixed points of symplcctic diffcomorphisms
    • MR876964 88b:58024
    • A. Floor. Morse theory for fixed points of symplcctic diffcomorphisms. Bull. Amer. Math. Soc. 16(2) (1987), 279-281. MR876964 (88b:58024)
    • (1987) Bull. Amer. Math. Soc , vol.16 , Issue.2 , pp. 279-281
    • Floor, A.1
  • 75
    • 11544255372 scopus 로고
    • Some physical consequences of vacuum polarization
    • L.L. Foldy, E. Eriksen. Some physical consequences of vacuum polarization. Phys. Rev. 95(4) (1954), 1048-1051.
    • (1954) Phys. Rev , vol.95 , Issue.4 , pp. 1048-1051
    • Foldy, L.L.1    Eriksen, E.2
  • 76
    • 0000961106 scopus 로고
    • Small amplitude solutions of the Maxwell-Dirac equations
    • MR1129332 92i:81107
    • V. Georgiev, Small amplitude solutions of the Maxwell-Dirac equations. Indiana Univ. Math. J. 40(3) (1991), 845-883. MR1129332 (92i:81107)
    • (1991) Indiana Univ. Math. J , vol.40 , Issue.3 , pp. 845-883
    • Georgiev, V.1
  • 78
    • 0007265659 scopus 로고
    • Vacuum polarization effects on energy levels in μ-mesonic atoms
    • R. Glauber, W. Rarita, P. Schwed. Vacuum polarization effects on energy levels in μ-mesonic atoms. Phys. Rev. 120(2) (1960), 609-613.
    • (1960) Phys. Rev , vol.120 , Issue.2 , pp. 609-613
    • Glauber, R.1    Rarita, W.2    Schwed, P.3
  • 79
    • 55849090595 scopus 로고    scopus 로고
    • W.T. Grandy, Jr. Relativistic quantum mechanics of leptons and fields. Kluwer Acad. Publisher, Fund. Theories of Physics, 41.
    • W.T. Grandy, Jr. Relativistic quantum mechanics of leptons and fields. Kluwer Acad. Publisher, Fund. Theories of Physics, Vol. 41.
  • 80
    • 55849142508 scopus 로고    scopus 로고
    • M. Griesemer, R.T. Lewis, H. Siedentop. A minimax principle in spectral gaps: Dirac operators with Coulomb potentials. Doc. Math. 4 (1999), 275-283 (electronic). MR1701887 (2000g:47023)
    • M. Griesemer, R.T. Lewis, H. Siedentop. A minimax principle in spectral gaps: Dirac operators with Coulomb potentials. Doc. Math. 4 (1999), 275-283 (electronic). MR1701887 (2000g:47023)
  • 81
    • 0000060563 scopus 로고    scopus 로고
    • M. Griesemer, H. Siedentop. A minimax principle for the eigenvalues in spectral gaps. J. London Math. Soc. 60(2) (1999), 490-500. MR1724845 (2000i:47047)
    • M. Griesemer, H. Siedentop. A minimax principle for the eigenvalues in spectral gaps. J. London Math. Soc. 60(2) (1999), 490-500. MR1724845 (2000i:47047)
  • 82
    • 84981754205 scopus 로고
    • The Cauchy problem for the coupled Maxwell and Dirac equations
    • MR0190520 32:7932
    • L. Gross. The Cauchy problem for the coupled Maxwell and Dirac equations. Comm. Pure Appl. Math. 19 (1966), 1-5. MR0190520 (32:7932)
    • (1966) Comm. Pure Appl. Math , vol.19 , pp. 1-5
    • Gross, L.1
  • 83
    • 21244459255 scopus 로고    scopus 로고
    • C. Hainzl, M. Lewin, É. Séré. Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation. Comm. Math. Phys. 257(3) (2005), 515-562. MR2164942 (2006i:81123)
    • C. Hainzl, M. Lewin, É. Séré. Existence of a stable polarized vacuum in the Bogoliubov-Dirac-Fock approximation. Comm. Math. Phys. 257(3) (2005), 515-562. MR2164942 (2006i:81123)
  • 84
    • 18744362441 scopus 로고    scopus 로고
    • C. Hainzl, M. Lewin, É. Séré. Self-consistent solution for the polarized vacuum in a no-photon QED model, J. Phys. A: Math. and Gen. 38 (2005), 4483-4499. MR2147635 (2006e:81341)
    • C. Hainzl, M. Lewin, É. Séré. Self-consistent solution for the polarized vacuum in a no-photon QED model, J. Phys. A: Math. and Gen. 38 (2005), 4483-4499. MR2147635 (2006e:81341)
  • 85
    • 55849105844 scopus 로고    scopus 로고
    • C. Hainzl, M. Lewin, É. Séré. Existence of atoms and molecules in the mean-field approximation of no-photon Quantum Electrodynamics, Arch. Rat. Mech. Anal., to appear.
    • C. Hainzl, M. Lewin, É. Séré. Existence of atoms and molecules in the mean-field approximation of no-photon Quantum Electrodynamics, Arch. Rat. Mech. Anal., to appear.
  • 86
    • 33847745752 scopus 로고    scopus 로고
    • The mean-field approximation in Quantum Electrodynamics. The no-photon case
    • MR2290710
    • C. Hainzl, M. Lewin, J.P. Solovej. The mean-field approximation in Quantum Electrodynamics. The no-photon case. Comm. Pure Appl. Math. 80(4) (2007), 546-596. MR2290710
    • (2007) Comm. Pure Appl. Math , vol.80 , Issue.4 , pp. 546-596
    • Hainzl, C.1    Lewin, M.2    Solovej, J.P.3
  • 87
    • 36049041594 scopus 로고    scopus 로고
    • C. Hainzl, M. Lewin. É. Séré, J.P. Solovej. A minimization method for relativistic electrons in a mean-field approximation of Quantum Electrodynamics. Phys. Rev. A 76 (2007), 052104.
    • C. Hainzl, M. Lewin. É. Séré, J.P. Solovej. A minimization method for relativistic electrons in a mean-field approximation of Quantum Electrodynamics. Phys. Rev. A 76 (2007), 052104.
  • 88
    • 21644484828 scopus 로고    scopus 로고
    • C. Hainzl, M. Lewin, C. Sperber. Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation, Lett. Math. Phys. 72 (2005), 99-113. MR2154857 (2006b:81070)
    • C. Hainzl, M. Lewin, C. Sperber. Existence of global-in-time solutions to a generalized Dirac-Fock type evolution equation, Lett. Math. Phys. 72 (2005), 99-113. MR2154857 (2006b:81070)
  • 89
    • 34250935804 scopus 로고
    • Bemerkungen zur Diracschen Theorie des Positrons.
    • W. Heisenberg. Bemerkungen zur Diracschen Theorie des Positrons. Z. Phys. 90 (1934), 209-223.
    • (1934) Z. Phys , vol.90 , pp. 209-223
    • Heisenberg, W.1
  • 90
    • 33744562453 scopus 로고
    • Doubts and hopes in quantum electrohydrodynamics
    • MR0058472 15:378f
    • W. Heisenberg. Doubts and hopes in quantum electrohydrodynamics. Physica 19 (1953), 897-908. MR0058472 (15:378f)
    • (1953) Physica , vol.19 , pp. 897-908
    • Heisenberg, W.1
  • 91
    • 0000461263 scopus 로고
    • 2/r
    • MR0436854 55:9790
    • 2/r. Comm. Math. Phys. 53 (1977), 285-294. MR0436854 (55:9790)
    • (1977) Comm. Math. Phys , vol.53 , pp. 285-294
    • Herbst, I.W.1
  • 92
    • 0038329564 scopus 로고
    • A solution to the problem of variational collapse for the one-particle Dirac equation
    • R.N. Hill, C. Krauthauser. A solution to the problem of variational collapse for the one-particle Dirac equation. Phys. Rev. Lett. 72(14) (1994), 2151-2154.
    • (1994) Phys. Rev. Lett , vol.72 , Issue.14 , pp. 2151-2154
    • Hill, R.N.1    Krauthauser, C.2
  • 93
    • 0001093993 scopus 로고
    • First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems
    • MR1079873 91m:58064
    • H. Hofer, K. Wysocki. First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems. Math. Ann. 288 (1990), 483-503. MR1079873 (91m:58064)
    • (1990) Math. Ann , vol.288 , pp. 483-503
    • Hofer, H.1    Wysocki, K.2
  • 94
    • 33847331309 scopus 로고    scopus 로고
    • M. Huber, H. Siedento Solutions of the Dirac-Fock equations and the energy of the electron-positron field. Arch. Rat. Mech. Anal. 184 (1) (2007), 1-22. MR2289861 (2007m:81065)
    • M. Huber, H. Siedento Solutions of the Dirac-Fock equations and the energy of the electron-positron field. Arch. Rat. Mech. Anal. 184 (1) (2007), 1-22. MR2289861 (2007m:81065)
  • 95
    • 0040676511 scopus 로고
    • On the spectra of Schrödinger multiparticle Hamiltonians
    • MR0211711 35:2588
    • W. Hunziker. On the spectra of Schrödinger multiparticle Hamiltonians. Helv. Phys. Acta. 39 (1966), 451-462. MR0211711 (35:2588)
    • (1966) Helv. Phys. Acta , vol.39 , pp. 451-462
    • Hunziker, W.1
  • 96
    • 0034397412 scopus 로고    scopus 로고
    • W. Hunziker, I.M. Sigel. The quantum N-body problem. J. Math. Phys. 41(6) (2000), 3448-3510. MR1768629 (2001g:81267)
    • W. Hunziker, I.M. Sigel. The quantum N-body problem. J. Math. Phys. 41(6) (2000), 3448-3510. MR1768629 (2001g:81267)
  • 99
    • 0043000410 scopus 로고
    • Holomorphic families of Dirac operators
    • MR706397 84k:35114
    • T. Kato. Holomorphic families of Dirac operators. Math. Z. 183(3) (1983), 399-406. MR706397 (84k:35114)
    • (1983) Math. Z , vol.183 , Issue.3 , pp. 399-406
    • Kato, T.1
  • 100
    • 84990619688 scopus 로고
    • Global existence of small amplitude solutions to the nonlinear Klein-Gordon equations in four space dimensions
    • MR803252 87e:35080
    • S. Klainerman. Global existence of small amplitude solutions to the nonlinear Klein-Gordon equations in four space dimensions. Comm. Pure Appl. Math. 38 (1985), 631-641. MR803252 (87e:35080)
    • (1985) Comm. Pure Appl. Math , vol.38 , pp. 631-641
    • Klainerman, S.1
  • 101
    • 0000870142 scopus 로고
    • The null condition and global existence to nonlinear wave equations
    • MR837683 87h:35217
    • S. Klainerman. The null condition and global existence to nonlinear wave equations. Lect. in Appl. Math. 23 (1986), 293-326. MR837683 (87h:35217)
    • (1986) Lect. in Appl. Math , vol.23 , pp. 293-326
    • Klainerman, S.1
  • 103
    • 0042887938 scopus 로고
    • Characterization and uniqueness of distinguished self-adjoint extensions of Dirac operators
    • MR519923 80k:81025
    • M. Klaus, R. Wüst. Characterization and uniqueness of distinguished self-adjoint extensions of Dirac operators. Comm. Math. Phys. 64(2) (1978-79), 171-176. MR519923 (80k:81025)
    • (1978) Comm. Math. Phys , vol.64 , Issue.2 , pp. 171-176
    • Klaus, M.1    Wüst, R.2
  • 104
    • 84990631940 scopus 로고
    • Basis set expansion of the Dirac operator without variational collapse
    • W. Kutzelnigg. Basis set expansion of the Dirac operator without variational collapse. Int. J. Quant. Chem. 25 (1984), 107-129.
    • (1984) Int. J. Quant. Chem , vol.25 , pp. 107-129
    • Kutzelnigg, W.1
  • 105
    • 0031321343 scopus 로고    scopus 로고
    • Relativistic one-electron Hamiltonians "for electrons only" and the variational treatment of the Dirac equation
    • W. Kutzelnigg. Relativistic one-electron Hamiltonians "for electrons only" and the variational treatment of the Dirac equation. Chemical Physics 225 (1997), 203-222.
    • (1997) Chemical Physics , vol.225 , pp. 203-222
    • Kutzelnigg, W.1
  • 106
    • 84968486001 scopus 로고
    • Uniqueness of radial solutions of semilinear elliptic equations
    • MR1088021 92k:35102
    • M.K. Kwong, Y. Li. Uniqueness of radial solutions of semilinear elliptic equations. Trans. Amer. Math. Soc. 333 (1992), 339-363. MR1088021 (92k:35102)
    • (1992) Trans. Amer. Math. Soc , vol.333 , pp. 339-363
    • Kwong, M.K.1    Li, Y.2
  • 107
    • 18744380728 scopus 로고
    • On the quantum theory of fields
    • Pergamon Press, Oxford, Reprinted in Collected papers of L.D. Landau, edited by D. Ter Haar, Pergamon Press, 1965. MR0075092 17:692f
    • L.D. Landau. On the quantum theory of fields. Bohr Volume, Pergamon Press, Oxford, 1955. Reprinted in Collected papers of L.D. Landau, edited by D. Ter Haar, Pergamon Press, 1965. MR0075092 (17:692f)
    • (1955) Bohr Volume
    • Landau, L.D.1
  • 108
    • 19844378167 scopus 로고    scopus 로고
    • C. Le Bris, P.-L. Lions. From atoms to crystals: a mathematical journey. Bull. Amer. Math. Soc. (N.S.) 42(3) (2005), 291-363. MR2149087 (2006k:81121)
    • C. Le Bris, P.-L. Lions. From atoms to crystals: a mathematical journey. Bull. Amer. Math. Soc. (N.S.) 42(3) (2005), 291-363. MR2149087 (2006k:81121)
  • 109
    • 0009169949 scopus 로고
    • Solving the Dirac equation, using the large component only, in a Dirac-type Slater orbital basis set
    • E. van Lenthe, E.J. Baerends, J.G. Snijders. Solving the Dirac equation, using the large component only, in a Dirac-type Slater orbital basis set. Chem. Phys. Lett. 238 (1995), 235-241.
    • (1995) Chem. Phys. Lett , vol.238 , pp. 235-241
    • van Lenthe, E.1    Baerends, E.J.2    Snijders, J.G.3
  • 110
    • 0346733621 scopus 로고
    • Relativistic regular two-component Hamiltonians
    • R. Brock et al ed. Publications Dept. Chem. Phys. and Material sciences. University of Groningen
    • E. van Lenthe, R. van Leeuwen, E.J. Baerends, J.G. Snijders. Relativistic regular two-component Hamiltonians. In New challenges in computational Quantum Chemistry. R. Brock et al ed. Publications Dept. Chem. Phys. and Material sciences. University of Groningen, 1994.
    • (1994) New challenges in computational Quantum Chemistry
    • van Lenthe, E.1    van Leeuwen, R.2    Baerends, E.J.3    Snijders, J.G.4
  • 111
    • 36449004665 scopus 로고
    • Exact solutions of regular approximate relativistic wave equations for hydrogen-like atoms
    • R. van Leeuwen, E. van Lenthe, E.J. Baerends, J.G. Snijders. Exact solutions of regular approximate relativistic wave equations for hydrogen-like atoms. J. Chem. Phys. 101(2) (1994), 1272-1281.
    • (1994) J. Chem. Phys , vol.101 , Issue.2 , pp. 1272-1281
    • van Leeuwen, R.1    van Lenthe, E.2    Baerends, E.J.3    Snijders, J.G.4
  • 113
    • 0000681089 scopus 로고
    • Variational principle for many-fermion systems
    • MR601336 81m:81083
    • E.H. Lieb. Variational principle for many-fermion systems. Phys. Rev. Lett. 46 (1981), 457-459. MR601336 (81m:81083)
    • (1981) Phys. Rev. Lett , vol.46 , pp. 457-459
    • Lieb, E.H.1
  • 114
    • 0001231983 scopus 로고
    • On the lowest eigenvalue of the Laplacian for the intersection of two domains
    • MR724014 85e:35090
    • E.H. Lieb. On the lowest eigenvalue of the Laplacian for the intersection of two domains. Invent. Math. 74(3) (1983), 441-448. MR724014 (85e:35090)
    • (1983) Invent. Math , vol.74 , Issue.3 , pp. 441-448
    • Lieb, E.H.1
  • 115
    • 3342981749 scopus 로고
    • Bound on the maximum negative ionization of atoms and molecules
    • E.H. Lieb. Bound on the maximum negative ionization of atoms and molecules. Phys. Rev. A. 29 (1984), 3018-3028.
    • (1984) Phys. Rev. A , vol.29 , pp. 3018-3028
    • Lieb, E.H.1
  • 116
    • 0034349420 scopus 로고    scopus 로고
    • E.H. Lieb, H. Siedentop. Renormalization of the regularized relativistic electron-positron field. Comm. Math. Phys. 213(3) (2000), 673-683. MR1785433 (2001i:81175)
    • E.H. Lieb, H. Siedentop. Renormalization of the regularized relativistic electron-positron field. Comm. Math. Phys. 213(3) (2000), 673-683. MR1785433 (2001i:81175)
  • 117
    • 0000368619 scopus 로고
    • The Hartrec-Fock theory for Coulomb systems
    • MR0452286 56:10566
    • E. H. Lieb, B. Simon. The Hartrec-Fock theory for Coulomb systems. Comm. Math. Phys., 53 (1977), 185-194. MR0452286 (56:10566)
    • (1977) Comm. Math. Phys , vol.53 , pp. 185-194
    • Lieb, E.H.1    Simon, B.2
  • 118
    • 85030707196 scopus 로고
    • The concentration-compactness method in the Calculus of Variations. The locally compact case. Part. I
    • P.-L. Lions. The concentration-compactness method in the Calculus of Variations. The locally compact case. Part. I: Ann. Inst. H. Poincaré Anal. Nonlinéaire 1 (1984), 109-145.
    • (1984) Ann. Inst. H. Poincaré Anal. Nonlinéaire , vol.1 , pp. 109-145
    • Lions, P.-L.1
  • 119
    • 85030719142 scopus 로고    scopus 로고
    • Part. II: Ann. Inst. H. Poincaré Anal. Nonlinéaire 1 (1984), 223-283.
    • Part. II: Ann. Inst. H. Poincaré Anal. Nonlinéaire 1 (1984), 223-283.
  • 120
    • 0001929193 scopus 로고
    • Solutions of Hartree-Fock equations for Coulomb systems
    • MR879032 88e:35170
    • P.-L. Lions. Solutions of Hartree-Fock equations for Coulomb systems. Comm. Math. Phys. 109 (1987), 33-97. MR879032 (88e:35170)
    • (1987) Comm. Math. Phys , vol.109 , pp. 33-97
    • Lions, P.-L.1
  • 121
    • 21844507076 scopus 로고
    • A solitary wave solution of the Maxwell-Dirac equations
    • MR1364144 96k:81079
    • A.G. Lisi. A solitary wave solution of the Maxwell-Dirac equations. J. Phys. A 28(18) (1995), 5385-5392. MR1364144 (96k:81079)
    • (1995) J. Phys. A , vol.28 , Issue.18 , pp. 5385-5392
    • Lisi, A.G.1
  • 122
    • 85157193294 scopus 로고    scopus 로고
    • S. Machihara, K. Nakanishi, T. Ozawa. Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation. Rev. Mat. Iberoamericana 19(1) (2003), 179-194. MR1993419 (2005h:35293)
    • S. Machihara, K. Nakanishi, T. Ozawa. Small global solutions and the nonrelativistic limit for the nonlinear Dirac equation. Rev. Mat. Iberoamericana 19(1) (2003), 179-194. MR1993419 (2005h:35293)
  • 123
    • 0037242247 scopus 로고    scopus 로고
    • N. Masmoudi, K. Nakanishi. Nonrelativistic limit from Maxwell-Klein-Gordon and Maxwell-Dirac to Poisson-Schrödinger. Int. Math. Res. Not. 13 (2003), 697-734. MR1949296 (2004b:81042)
    • N. Masmoudi, K. Nakanishi. Nonrelativistic limit from Maxwell-Klein-Gordon and Maxwell-Dirac to Poisson-Schrödinger. Int. Math. Res. Not. 13 (2003), 697-734. MR1949296 (2004b:81042)
  • 124
    • 0344982994 scopus 로고    scopus 로고
    • N. Masmoudi, K. Nakanishi. Uniqueness of Finite Energy Solutions for Maxwell-Dirac and Maxwell-Klein-Gordon Equations. Comm. Math. Phys. 243 (2003), 123-136. MR2020223 (2004i:81060)
    • N. Masmoudi, K. Nakanishi. Uniqueness of Finite Energy Solutions for Maxwell-Dirac and Maxwell-Klein-Gordon Equations. Comm. Math. Phys. 243 (2003), 123-136. MR2020223 (2004i:81060)
  • 125
    • 0002577676 scopus 로고
    • Existence of stationary states for nonlinear Dirac equations
    • MR949625 89k:81027
    • F. Merle. Existence of stationary states for nonlinear Dirac equations. J. Differential Equations 74(1) (1988), 50-68. MR949625 (89k:81027)
    • (1988) J. Differential Equations , vol.74 , Issue.1 , pp. 50-68
    • Merle, F.1
  • 126
    • 26744434516 scopus 로고
    • Theory of relativistic effects on atoms: Configuration-space Hamiltonian
    • M.H. Mittleman. Theory of relativistic effects on atoms: Configuration-space Hamiltonian. Phys. Rev. A 24(3) (1981), 1167-1175.
    • (1981) Phys. Rev. A , vol.24 , Issue.3 , pp. 1167-1175
    • Mittleman, M.H.1
  • 127
    • 0031617276 scopus 로고    scopus 로고
    • QED corrections in heavy atoms
    • P. J. Mohr, G. Plunien, G. Soff. QED corrections in heavy atoms. Phys. Rep. 293(5&6) (1998), 227-372.
    • (1998) Phys. Rep , vol.293 , Issue.5-6 , pp. 227-372
    • Mohr, P.J.1    Plunien, G.2    Soff, G.3
  • 128
    • 85012912563 scopus 로고
    • The nonrelativistic limit of the nonlinear Dirac equation
    • MR1151464 93b:81047
    • B. Najrnan. The nonrelativistic limit of the nonlinear Dirac equation. Ann. Inst. H. Poincaré Anal. Non Linéaire 9(1) (1992), 3-12. MR1151464 (93b:81047)
    • (1992) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.9 , Issue.1 , pp. 3-12
    • Najrnan, B.1
  • 129
    • 0040845487 scopus 로고
    • Self-adjointness and invariance of the essential spectrum for Dirac operators defined as quadratic forms
    • MR0421456 54:9459
    • G. Nenciu. Self-adjointness and invariance of the essential spectrum for Dirac operators defined as quadratic forms. Comm. Math. Phys. 48 (1976). 235-247. MR0421456 (54:9459)
    • (1976) Comm. Math. Phys , vol.48 , pp. 235-247
    • Nenciu, G.1
  • 130
    • 0040616496 scopus 로고
    • Existence of spontaneous pair creation in the external field approximation of Q.E.D
    • MR880417 89b:81271
    • G. Nenciu. Existence of spontaneous pair creation in the external field approximation of Q.E.D., Comm. Math. Phys. 109 (1987), 303-312. MR880417 (89b:81271)
    • (1987) Comm. Math. Phys , vol.109 , pp. 303-312
    • Nenciu, G.1
  • 131
    • 55849121474 scopus 로고    scopus 로고
    • H. Ounaics. Perturbation method for a class of nonlinear Dirac equations. Differential Integral Equations 13(4-6) (2000), 707-720. MR1750047 (2001a:35150)
    • H. Ounaics. Perturbation method for a class of nonlinear Dirac equations. Differential Integral Equations 13(4-6) (2000), 707-720. MR1750047 (2001a:35150)
  • 132
    • 0034345506 scopus 로고    scopus 로고
    • E. Paturel. Solutions of the Dirac equations without projector. Ann. Henri Poincaré 1 (2000), 1123-1157. MR12309795 (2001k:81369)
    • E. Paturel. Solutions of the Dirac equations without projector. Ann. Henri Poincaré 1 (2000), 1123-1157. MR12309795 (2001k:81369)
  • 133
    • 55849127720 scopus 로고    scopus 로고
    • P. Pickl. Existence of Spontaneous Pair Creation. Dissertiation. München (2005), arXiv:hep-th/0609200.
    • P. Pickl. Existence of Spontaneous Pair Creation. Dissertiation. München (2005), arXiv:hep-th/0609200.
  • 134
    • 18744378631 scopus 로고
    • Vanishing of renormalized charges in field theories with point interaction
    • MR0082374 18:541a
    • I.Ya Pomeranchuk, V.V. Sudakov, K.A. Ter-Martirosyan. Vanishing of renormalized charges in field theories with point interaction. Phys. Rev. 103 (3) (1956), 784-802. MR0082374 (18:541a)
    • (1956) Phys. Rev , vol.103 , Issue.3 , pp. 784-802
    • Ya Pomeranchuk, I.1    Sudakov, V.V.2    Ter-Martirosyan, K.A.3
  • 135
    • 84980131053 scopus 로고
    • Free vibrations for a semilinear wave equation
    • MR470378 81i:35109
    • P.H. Rabinowitz. Free vibrations for a semilinear wave equation. Comm. Pure Appl. Math. 31(1) (1978), 31-68. MR470378 (81i:35109)
    • (1978) Comm. Pure Appl. Math , vol.31 , Issue.1 , pp. 31-68
    • Rabinowitz, P.H.1
  • 136
    • 84980196930 scopus 로고
    • Periodic solutions of Hamiltonian systems
    • MR0467823 57:7674
    • P.H. Rabinowitz. Periodic solutions of Hamiltonian systems. Comm. Pure Appl. Math. 31(2) (1978), 157-184. MR0467823 (57:7674)
    • (1978) Comm. Pure Appl. Math , vol.31 , Issue.2 , pp. 157-184
    • Rabinowitz, P.H.1
  • 137
    • 0030518383 scopus 로고    scopus 로고
    • Localized solutions of the Dirac-Maxwell equations
    • MR1408100 97g:81076
    • C.J. Radford. Localized solutions of the Dirac-Maxwell equations. J. Math. Phys. 37(9) (1996), 4418-4433. MR1408100 (97g:81076)
    • (1996) J. Math. Phys , vol.37 , Issue.9 , pp. 4418-4433
    • Radford, C.J.1
  • 138
    • 0038176530 scopus 로고    scopus 로고
    • C.J. Radford. The stationary Maxwell-Dirac equations. J. Phys. A 36(20) (2008), 5663-5681. MR1985533 (2004i:81268)
    • C.J. Radford. The stationary Maxwell-Dirac equations. J. Phys. A 36(20) (2008), 5663-5681. MR1985533 (2004i:81268)
  • 139
    • 55849108412 scopus 로고    scopus 로고
    • A.F. Rañada. Classical nonlinear Dirac field models of extended particles. In Quantum theory. groups, fields and particles (editor A.O. Barut). Reidel, Amsterdam (1982).
    • A.F. Rañada. Classical nonlinear Dirac field models of extended particles. In Quantum theory. groups, fields and particles (editor A.O. Barut). Reidel, Amsterdam (1982).
  • 140
    • 0039810296 scopus 로고
    • Abstract non-linear wave equations
    • Springer-Verlag, Berlin, MR0605679 58:29290
    • M. Reed. Abstract non-linear wave equations. Lecture Notes in Math. 507, Springer-Verlag, Berlin. 1976. MR0605679 (58:29290)
    • (1976) Lecture Notes in Math , vol.507
    • Reed, M.1
  • 141
    • 0003276274 scopus 로고
    • Methods of modern mathematical physics, Vol. 4
    • 58:12429c, New York
    • M. Reed, B. Simon. Methods of modern mathematical physics, Vol. 4. Academic Press, New York. 1978. MR0493421 (58:12429c)
    • (1978) Academic Press
    • Reed, M.1    Simon, B.2
  • 142
    • 0000043934 scopus 로고
    • Quantum Electrodynamics of strong fields
    • J. Reinhardt, W. Greiner. Quantum Electrodynamics of strong fields. Rep. Prog. Phys. 40 (1977), 219-295.
    • (1977) Rep. Prog. Phys , vol.40 , pp. 219-295
    • Reinhardt, J.1    Greiner, W.2
  • 144
    • 0002248799 scopus 로고
    • Theory of positron production in heavy-ion collision
    • J. Reinhardt, B. Müller, W. Greiner. Theory of positron production in heavy-ion collision. Phys. Rev. A, 24(1) (1981), 103-128.
    • (1981) Phys. Rev. A , vol.24 , Issue.1 , pp. 103-128
    • Reinhardt, J.1    Müller, B.2    Greiner, W.3
  • 145
    • 0009407934 scopus 로고
    • Absence of discrete spectrum in highly negative ions. II. Extension to fermions
    • MR676005 84b:81124
    • M.B. Ruskai. Absence of discrete spectrum in highly negative ions. II. Extension to fermions. Comm. Math. Phys. 85(2) (1982), 325-327. MR676005 (84b:81124)
    • (1982) Comm. Math. Phys , vol.85 , Issue.2 , pp. 325-327
    • Ruskai, M.B.1
  • 146
    • 0002957091 scopus 로고
    • The existence of minimal immersions of 2-spheres
    • MR604040 82f:58035
    • J. Sacks, K. Uhlenbeck. The existence of minimal immersions of 2-spheres. Ann. of Math. 113(1) (1981), 1-24. MR604040 (82f:58035)
    • (1981) Ann. of Math , vol.113 , Issue.1 , pp. 1-24
    • Sacks, J.1    Uhlenbeck, K.2
  • 147
    • 0040803257 scopus 로고
    • Distinguished self-adjoint extensions of Dirac operators
    • MR0326448 48:4792
    • U.W. Schmincke. Distinguished self-adjoint extensions of Dirac operators. Math. Z. 129 (1972), 335-349. MR0326448 (48:4792)
    • (1972) Math. Z , vol.129 , pp. 335-349
    • Schmincke, U.W.1
  • 148
    • 36149023636 scopus 로고    scopus 로고
    • J. Schwinger. Quantum Electrodynamics I. A covariant formulation. Phys. Rev. 74(10) (1948), 1439-1461. MR0027714 (10:345b)
    • J. Schwinger. Quantum Electrodynamics I. A covariant formulation. Phys. Rev. 74(10) (1948), 1439-1461. MR0027714 (10:345b)
  • 149
    • 36149012875 scopus 로고    scopus 로고
    • J. Schwinger. Quantum Electrodynamics II. Vacuum polarization and self-energy. Phys. Rev. 75(4) (1949), 651-679. MR0029780 (10:663b)
    • J. Schwinger. Quantum Electrodynamics II. Vacuum polarization and self-energy. Phys. Rev. 75(4) (1949), 651-679. MR0029780 (10:663b)
  • 150
    • 0347162275 scopus 로고
    • On gauge invariance and vacuum polarization
    • 66.4-679. MR0041727 12:889c
    • J. Schwinger. On gauge invariance and vacuum polarization. Phys. Rev. II. Ser. 82(5) (1951), 66.4-679. MR0041727 (12:889c)
    • (1951) Phys. Rev. II. Ser , vol.82 , Issue.5
    • Schwinger, J.1
  • 151
    • 21844483031 scopus 로고
    • 2N, of restricted contact type
    • MR1350410 96h:58027
    • 2N, of restricted contact type. Comm. Math. Phys. 172(2) (1995), 293-316. MR1350410 (96h:58027)
    • (1995) Comm. Math. Phys , vol.172 , Issue.2 , pp. 293-316
    • Séré, E.1
  • 152
    • 34250234449 scopus 로고
    • Geometric methods in the quantum many-body problem. Nonexistence of very negative ions
    • MR676004 83m:81117
    • I.M. Sigal. Geometric methods in the quantum many-body problem. Nonexistence of very negative ions. Comm. Math. Phys. 85(2) (1982), 309-324. MR676004 (83m:81117)
    • (1982) Comm. Math. Phys , vol.85 , Issue.2 , pp. 309-324
    • Sigal, I.M.1
  • 153
    • 0040220853 scopus 로고
    • How many electrons can a nucleus bind?
    • MR768234 86a:81097
    • I.M. Sigal. How many electrons can a nucleus bind? Ann. of Phys. 157 (1984), 307-320. MR768234 (86a:81097)
    • (1984) Ann. of Phys , vol.157 , pp. 307-320
    • Sigal, I.M.1
  • 154
    • 0001146482 scopus 로고
    • An infinite dimensional version of Sard's Theorem
    • MR0185604 32:3067
    • S. Smale. An infinite dimensional version of Sard's Theorem. Amer. J. Math. 87 (1965), 861-866. MR0185604 (32:3067)
    • (1965) Amer. J. Math , vol.87 , pp. 861-866
    • Smale, S.1
  • 155
    • 0000685546 scopus 로고
    • Classical, stable, nonlinear spinor field with positive rest energy
    • M. Soler. Classical, stable, nonlinear spinor field with positive rest energy. Phys. Rev. D 1 (1970), 2766-2769.
    • (1970) Phys. Rev. D , vol.1 , pp. 2766-2769
    • Soler, M.1
  • 156
    • 4244211971 scopus 로고
    • Stability under dilations of nonlinear spinor fields
    • MR848095 87g:81016
    • W.A. Strauss, L. Vazquez. Stability under dilations of nonlinear spinor fields. Phys. Rev. D 34(2) (1986), 641-643. MR848095 (87g:81016)
    • (1986) Phys. Rev. D , vol.34 , Issue.2 , pp. 641-643
    • Strauss, W.A.1    Vazquez, L.2
  • 157
    • 0001632642 scopus 로고
    • The relativistic self-consistent field
    • B. Swirles. The relativistic self-consistent field. Proc. Roy. Soc. A 152 (1935), 625-649.
    • (1935) Proc. Roy. Soc. A , vol.152 , pp. 625-649
    • Swirles, B.1
  • 158
    • 0001691788 scopus 로고    scopus 로고
    • W. Kryszewski, A. Szulkin. Generalized linking theorem with an application to a semilinear Schrödinger equation. Adv. Differential Equations 3(3) (1998), 441-472. MR1751952 (2001g:58021)
    • W. Kryszewski, A. Szulkin. Generalized linking theorem with an application to a semilinear Schrödinger equation. Adv. Differential Equations 3(3) (1998), 441-472. MR1751952 (2001g:58021)
  • 159
    • 0000291836 scopus 로고
    • Minimax principle for the Dirac equation
    • MR854208 87i:81039
    • J.D. Talman. Minimax principle for the Dirac equation. Phys. Rev. Lett. 57(9) (1986). 1091-1094. MR854208 (87i:81039)
    • (1986) Phys. Rev. Lett , vol.57 , Issue.9 , pp. 1091-1094
    • Talman, J.D.1
  • 160
    • 0003619310 scopus 로고
    • Springer-Verlag, MR1219537 94k:81056
    • B. Thaller. The Dirac Equation. Springer-Verlag, 1992. MR1219537 (94k:81056)
    • (1992) The Dirac Equation
    • Thaller, B.1
  • 161
    • 0001731072 scopus 로고    scopus 로고
    • Lower bound for the ground state energy of the no-pair Hamiltonian
    • MR1461249 98g:81036
    • C. Tix. Lower bound for the ground state energy of the no-pair Hamiltonian. Phys. Lett. B 405 (1997), 293-296. MR1461249 (98g:81036)
    • (1997) Phys. Lett. B , vol.405 , pp. 293-296
    • Tix, C.1
  • 162
    • 0001130659 scopus 로고    scopus 로고
    • Strict positivity of a relativistic Hamiltonian due to Brown and Ravenhall
    • MR1608118 99b:81047
    • C. Tix. Strict positivity of a relativistic Hamiltonian due to Brown and Ravenhall. Bull. London Math. Soc. 30(3) (1998), 283-290. MR1608118 (99b:81047)
    • (1998) Bull. London Math. Soc , vol.30 , Issue.3 , pp. 283-290
    • Tix, C.1
  • 163
    • 0001356193 scopus 로고    scopus 로고
    • Nontrivial solution of a semilinear Schrödinger equation
    • MR1410836 98i:35034
    • C. Troestler, M. Willem. Nontrivial solution of a semilinear Schrödinger equation. Comm. Partial Differential Equations 21(9-10) (1996), 1431-1449. MR1410836 (98i:35034)
    • (1996) Comm. Partial Differential Equations , vol.21 , Issue.9-10 , pp. 1431-1449
    • Troestler, C.1    Willem, M.2
  • 164
    • 0042220599 scopus 로고
    • Theory of finite systems of particles. I. The Green function
    • MR0201168 34:1052
    • C. Van Winter. Theory of finite systems of particles. I. The Green function. Mat.-Fys. Skr. Danske Vid. Selsk. 2(8) (1964). MR0201168 (34:1052)
    • (1964) Mat.-Fys. Skr. Danske Vid. Selsk , vol.2 , Issue.8
    • Van Winter, C.1
  • 165
    • 4243501306 scopus 로고
    • Localised solutions of a non-linear spinor field
    • MR0456046 56:14278
    • L. Vázquez. Localised solutions of a non-linear spinor field. J. Phys. A 10(8) (1977), 1361-1368. MR0456046 (56:14278)
    • (1977) J. Phys. A , vol.10 , Issue.8 , pp. 1361-1368
    • Vázquez, L.1
  • 166
    • 0040106290 scopus 로고
    • Finiteness of a discrete spectrum of many-particle Hamiltonians in symmetry spaces (coordinate and momentum representations)
    • MR0449304 56:7609
    • S.A. Vugalter, G.M. Zhislin. Finiteness of a discrete spectrum of many-particle Hamiltonians in symmetry spaces (coordinate and momentum representations). Teoret. Mat. Fiz. 32(1) (1977), 70-87. MR0449304 (56:7609)
    • (1977) Teoret. Mat. Fiz , vol.32 , Issue.1 , pp. 70-87
    • Vugalter, S.A.1    Zhislin, G.M.2
  • 167
    • 0002413122 scopus 로고
    • Intensely localized solutions of the classical Dirac-Maxwell field equations
    • M. Wakano. Intensely localized solutions of the classical Dirac-Maxwell field equations. Progr. Theor. Phys. 35(8) (1966), 1117-1141.
    • (1966) Progr. Theor. Phys , vol.35 , Issue.8 , pp. 1117-1141
    • Wakano, M.1
  • 168
    • 0008731594 scopus 로고
    • Use of the squared Dirac operator in variational relativistic calculations
    • H. Wallmeier, W. Kutzelnigg. Use of the squared Dirac operator in variational relativistic calculations. Chem. Phys. Lett. 78(2) (1981), 341-346.
    • (1981) Chem. Phys. Lett , vol.78 , Issue.2 , pp. 341-346
    • Wallmeier, H.1    Kutzelnigg, W.2
  • 169
    • 0000686130 scopus 로고
    • Modulational stability of ground states of nonlinear Schrödinger equations
    • MR783974 86i:35130
    • M.I. Weinstein. Modulational stability of ground states of nonlinear Schrödinger equations. SIAM J. Math. Anal 16(3) (1985), 472-491. MR783974 (86i:35130)
    • (1985) SIAM J. Math. Anal , vol.16 , Issue.3 , pp. 472-491
    • Weinstein, M.I.1
  • 170
    • 0007539583 scopus 로고
    • A remark on the coupling of gravitation and electron
    • MR0033250 11:410b
    • H. Weyl. A remark on the coupling of gravitation and electron. Phys. Rev. 77 (1950), 699-701. MR0033250 (11:410b)
    • (1950) Phys. Rev , vol.77 , pp. 699-701
    • Weyl, H.1
  • 171
    • 4243427955 scopus 로고
    • Dirac operations with strongly singular potentials. Distinguished self-adjoint extensions constructed with a spectral gap theorem and cut-off potentials
    • MR0437948 55:10869
    • R. Wüst. Dirac operations with strongly singular potentials. Distinguished self-adjoint extensions constructed with a spectral gap theorem and cut-off potentials. Math. Z. 152(3) (1977), 259-271. MR0437948 (55:10869)
    • (1977) Math. Z , vol.152 , Issue.3 , pp. 259-271
    • Wüst, R.1
  • 172
    • 0002870854 scopus 로고
    • A study of the spectrum of the Schrödinger operator for a system of several particles. (Russian)
    • MR0126729 23:A4023
    • G. M. Zhislin. A study of the spectrum of the Schrödinger operator for a system of several particles. (Russian) Trudy Moskov. Mat. Obščμ. 9 (1960), 81-120. MR0126729 (23:A4023)
    • (1960) Trudy Moskov. Mat. Obščμ , vol.9 , pp. 81-120
    • Zhislin, G.M.1
  • 173
    • 0009105302 scopus 로고
    • The spectrum of the energy operator for atoms with fixed nuclei on subspaces corresponding to irreducible representations of the group of permutations
    • G. M. Zhislin, A.G. Sigalov. The spectrum of the energy operator for atoms with fixed nuclei on subspaces corresponding to irreducible representations of the group of permutations. (Russian) Izv. Akad. Nauk SSSR Ser. Mat. 29 (1965), 835-860.
    • (1965) (Russian) Izv. Akad. Nauk SSSR Ser. Mat , vol.29 , pp. 835-860
    • Zhislin, G.M.1    Sigalov, A.G.2
  • 174
    • 55349096755 scopus 로고    scopus 로고
    • English translation, MR0194075 33:2289
    • Transl. Amer. Math. Soc. Ser. 2 91, 263-296 (English translation). MR0194075 (33:2289)
    • Transl. Amer. Math. Soc. Ser. 2 , vol.91 , pp. 263-296


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