메뉴 건너뛰기




Volumn 49, Issue 9, 2008, Pages

On Painlev́ VI transcendents related to the Dirac operator on the hyperbolic disk

Author keywords

[No Author keywords available]

Indexed keywords


EID: 54749137009     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2976218     Document Type: Article
Times cited : (8)

References (34)
  • 1
    • 36749106034 scopus 로고
    • Painlev́ functions of the third kind
    • 0022-2488 10.1063/1.523367.
    • McCoy, B. M., Tracy, C. A., and Wu, T. T., " Painlev́ functions of the third kind.," J. Math. Phys. 0022-2488 10.1063/1.523367 18, 1058 (1977).
    • (1977) J. Math. Phys. , vol.18 , pp. 1058
    • McCoy, B.M.1    Tracy, C.A.2    Wu, T.T.3
  • 2
    • 0000715867 scopus 로고
    • Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region
    • Wu, T. T., McCoy, B. M., Tracy, C. A., and Barouch, E., " Spin-spin correlation functions for the two-dimensional Ising model: Exact theory in the scaling region.," Phys. Rev. B 13, 316 (1976).
    • (1976) Phys. Rev. B , vol.13 , pp. 316
    • Wu, T.T.1    McCoy, B.M.2    Tracy, C.A.3    Barouch, E.4
  • 3
    • 85008290297 scopus 로고
    • Holonomic quantum fields I-IV
    • 0034-5318 10.2977/prims/1195189284, ();, " Publ. Res. Inst. Math. Sci. 0034-5318 10.2977/prims/1195188429 15, 201 (1979);, " Publ. Res. Inst. Math. Sci. 0034-5318 10.2977/prims/1195188185 15, 577 (1979);, " Publ. Res. Inst. Math. Sci. 15, 871 (1979).
    • Sato, M., Miwa, T., and Jimbo, M., " Holonomic quantum fields I-IV.," Publ. Res. Inst. Math. Sci. 0034-5318 10.2977/prims/1195189284 14, 223 (1978); Sato, M., Miwa, T., and Jimbo, M., " Publ. Res. Inst. Math. Sci. 0034-5318 10.2977/prims/1195188429 15, 201 (1979); Sato, M., Miwa, T., and Jimbo, M., " Publ. Res. Inst. Math. Sci. 0034-5318 10.2977/prims/1195188185 15, 577 (1979); Sato, M., Miwa, T., and Jimbo, M., " Publ. Res. Inst. Math. Sci. 15, 871 (1979).
    • (1978) Publ. Res. Inst. Math. Sci. , vol.14 , pp. 223
    • Sato, M.1    Miwa, T.2    Jimbo, M.3    Sato, M.4    Miwa, T.5    Jimbo, M.6    Sato, M.7    Miwa, T.8    Jimbo, M.9    Sato, M.10    Miwa, T.11    Jimbo, M.12
  • 4
    • 84972554199 scopus 로고
    • Tau functions for the Dirac operator in the Euclidean plane
    • Palmer, J., " Tau functions for the Dirac operator in the Euclidean plane.," Pac. J. Math. 160, 259 (1993).
    • (1993) Pac. J. Math. , vol.160 , pp. 259
    • Palmer, J.1
  • 5
    • 70449642006 scopus 로고    scopus 로고
    • Progress in Mathematical Physics Vol. (Birkhäuser, Boston).
    • Palmer, J., Planar Ising Correlations, Progress in Mathematical Physics Vol. 49 (Birkhäuser, Boston, 2007).
    • (2007) Planar Ising Correlations , vol.49
    • Palmer, J.1
  • 6
    • 0040914456 scopus 로고
    • Determinants of Cauchy-Riemann operators as τ -functions
    • 0167-8019 10.1007/BF00049126.
    • Palmer, J., " Determinants of Cauchy-Riemann operators as τ -functions.," Acta Appl. Math. 0167-8019 10.1007/BF00049126 18, 199 (1990).
    • (1990) Acta Appl. Math. , vol.18 , pp. 199
    • Palmer, J.1
  • 7
    • 33745635718 scopus 로고    scopus 로고
    • Point interactions in one dimension and holonomic quantum fields
    • Lisovyy, O., " Point interactions in one dimension and holonomic quantum fields.," Lett. Math. Phys. 77, 63 (2006); e-print arXiv:math-ph/0510095.
    • (2006) Lett. Math. Phys. , vol.77 , pp. 63
    • Lisovyy, O.1
  • 8
    • 21244485538 scopus 로고    scopus 로고
    • Tau functions for the Dirac operator on the cylinder
    • Lisovyy, O., " Tau functions for the Dirac operator on the cylinder.," Commun. Math. Phys. 255, 61 (2005); e-print arXiv:hep-th/0312277.
    • (2005) Commun. Math. Phys. , vol.255 , pp. 61
    • Lisovyy, O.1
  • 9
    • 79551490232 scopus 로고    scopus 로고
    • Nonlinear differential equations for the correlation functions of the 2D Ising model on the cylinder
    • Lisovyy, O., " Nonlinear differential equations for the correlation functions of the 2D Ising model on the cylinder.," Adv. Theor. Math. Phys. 5, 909 (2001); e-print arXiv:hep-th/0108015.
    • (2001) Adv. Theor. Math. Phys. , vol.5 , pp. 909
    • Lisovyy, O.1
  • 10
    • 3142692635 scopus 로고    scopus 로고
    • Spin matrix elements in 2D Ising model on the finite lattice
    • Bugrij, A. I. and Lisovyy, O., " Spin matrix elements in 2D Ising model on the finite lattice.," Phys. Lett. A 319, 390 (2003); e-print arXiv:0708.3625.
    • (2003) Phys. Lett. A , vol.319 , pp. 390
    • Bugrij, A.I.1    Lisovyy, O.2
  • 11
    • 3142734505 scopus 로고    scopus 로고
    • Correlation function of the two-dimensional Ising model on the finite lattice II
    • 0040-5779 10.1023/B:TAMP.0000033035.90327.1f, (); e-print arXiv:0708.3643.
    • Bugrij, A. I. and Lisovyy, O., " Correlation function of the two-dimensional Ising model on the finite lattice II.," Theor. Math. Phys. 0040-5779 10.1023/B:TAMP.0000033035.90327.1f 140, 987 (2004); e-print arXiv:0708.3643.
    • (2004) Theor. Math. Phys. , vol.140 , pp. 987
    • Bugrij, A.I.1    Lisovyy, O.2
  • 12
    • 0037279605 scopus 로고    scopus 로고
    • Ising field theory in a magnetic field: Analytic properties of the free energy
    • 0022-4715 10.1023/A:1022147532606, (); e-print arXiv:hep-th/0112167.
    • Fonseca, P. and Zamolodchikov, A., " Ising field theory in a magnetic field: Analytic properties of the free energy.," J. Stat. Phys. 0022-4715 10.1023/A:1022147532606 110, 527 (2003); e-print arXiv:hep-th/0112167.
    • (2003) J. Stat. Phys. , vol.110 , pp. 527
    • Fonseca, P.1    Zamolodchikov, A.2
  • 13
    • 29044450270 scopus 로고    scopus 로고
    • Finite-temperature form factors in the free Majorana theory
    • e-print arXiv:hep-th/0506105.
    • Doyon, B., " Finite-temperature form factors in the free Majorana theory.," J. Stat. Mech.: Theory Exp. 2005, P11006; e-print arXiv:hep-th/0506105.
    • J. Stat. Mech.: Theory Exp. , vol.2005 , pp. 11006
    • Doyon, B.1
  • 14
    • 21844499558 scopus 로고
    • Tau functions for the Dirac operator on the Poincaŕ disk
    • 0010-3616 10.1007/BF02099740, (); e-print arXiv:hep-th/9309017.
    • Palmer, J., Beatty, M., and Tracy, C. A., " Tau functions for the Dirac operator on the Poincaŕ disk.," Commun. Math. Phys. 0010-3616 10.1007/BF02099740 165, 97 (1994); e-print arXiv:hep-th/9309017.
    • (1994) Commun. Math. Phys. , vol.165 , pp. 97
    • Palmer, J.1    Beatty, M.2    Tracy, C.A.3
  • 15
    • 1542477549 scopus 로고
    • Holonomic quantum field theory of bosons in the Poincaŕ disk and the zero curvature limit
    • 0550-3213 10.1016/0550-3213(90)90459-Q.
    • Narayanan, R. and Tracy, C. A., " Holonomic quantum field theory of bosons in the Poincaŕ disk and the zero curvature limit.," Nucl. Phys. B 0550-3213 10.1016/0550-3213(90)90459-Q 340, 568 (1990).
    • (1990) Nucl. Phys. B , vol.340 , pp. 568
    • Narayanan, R.1    Tracy, C.A.2
  • 16
    • 21244499245 scopus 로고
    • in, Contemporary Mathematics Vol., edited by M. S. Berger (American Mathematics Society, Providence, RI)
    • Palmer, J. and Tracy, C. A., in Mathematics of Nonlinear Science, Contemporary Mathematics Vol. 108, edited by, M. S. Berger, (American Mathematics Society, Providence, RI, 1990), pp. 119-131.
    • (1990) Mathematics of Nonlinear Science , vol.108 , pp. 119-131
    • Palmer, J.1    Tracy, C.A.2
  • 17
    • 0242595782 scopus 로고    scopus 로고
    • Two-point correlation functions of scaling fields in the Dirac theory on the Poincare disk
    • 0550-3213 10.1016/j.nuclphysb.2003.09.021, (); e-print arXiv:hep-th/0304190.
    • Doyon, B., " Two-point correlation functions of scaling fields in the Dirac theory on the Poincare disk.," Nucl. Phys. B 0550-3213 10.1016/j.nuclphysb.2003.09.021, 675, 607 (2003); e-print arXiv:hep-th/0304190.
    • (2003) Nucl. Phys. B , vol.675 , pp. 607
    • Doyon, B.1
  • 18
    • 0742323576 scopus 로고    scopus 로고
    • Form factors of Ising spin and disorder fields on the Poincaŕ disk
    • 0305-4470 10.1088/0305-4470/37/2/007.
    • Doyon, B., " Form factors of Ising spin and disorder fields on the Poincaŕ disk.," J. Phys. A 0305-4470 10.1088/0305-4470/37/2/007 37, 359 (2004).
    • (2004) J. Phys. A , vol.37 , pp. 359
    • Doyon, B.1
  • 19
    • 84901058473 scopus 로고    scopus 로고
    • Ising field theory on a pseudosphere
    • e-print arXiv:hep-th/0404136.
    • Doyon, B. and Fonseca, P., " Ising field theory on a pseudosphere.," J. Stat. Mech.: Theory Exp. 2004, P002; e-print arXiv:hep-th/0404136.
    • J. Stat. Mech.: Theory Exp. , vol.2004 , pp. 002
    • Doyon, B.1    Fonseca, P.2
  • 20
    • 34249872701 scopus 로고    scopus 로고
    • Aharonov-Bohm effect on the Poincaŕ disk
    • 0022-2488 10.1063/1.2738751, (); e-print arXiv:math-ph/0702066.
    • Lisovyy, O., " Aharonov-Bohm effect on the Poincaŕ disk.," J. Math. Phys. 0022-2488 10.1063/1.2738751 48, 052112 (2007); e-print arXiv:math-ph/0702066.
    • (2007) J. Math. Phys. , vol.48 , pp. 052112
    • Lisovyy, O.1
  • 22
    • 0035907217 scopus 로고    scopus 로고
    • Hamiltonian self-adjoint extensions for (2+1) -dimensional Dirac particles
    • 0305-4470 10.1088/0305-4470/34/19/312, (); e-print arXiv:math-ph/0009008.
    • Falomir, H. and Pisani, P. A. G., " Hamiltonian self-adjoint extensions for (2+1) -dimensional Dirac particles.," J. Phys. A 0305-4470 10.1088/0305-4470/34/19/312 34, 4143 (2001); e-print arXiv:math-ph/0009008.
    • (2001) J. Phys. A , vol.34 , pp. 4143
    • Falomir, H.1    Pisani, P.A.G.2
  • 23
    • 0001594478 scopus 로고
    • Fermions in an Aharonov-Bohm field and cosmic strings
    • 0556-2821 10.1103/PhysRevD.40.1346.
    • Gerbert, Ph. de Sousa, " Fermions in an Aharonov-Bohm field and cosmic strings.," Phys. Rev. D 0556-2821 10.1103/PhysRevD.40.1346 40, 1346 (1989).
    • (1989) Phys. Rev. D , vol.40 , pp. 1346
    • Gerbert, Ph.D.S.1
  • 24
    • 2542591602 scopus 로고    scopus 로고
    • Green functions of the Dirac equation with magnetic-solenoid field
    • 0022-2488 10.1063/1.1699483, (); e-print arXiv:math-ph/0310007.
    • Gavrilov, S. P., Gitman, D. M., and Smirnov, A. A., " Green functions of the Dirac equation with magnetic-solenoid field.," J. Math. Phys. 0022-2488 10.1063/1.1699483 45, 1873 (2004); e-print arXiv:math-ph/ 0310007.
    • (2004) J. Math. Phys. , vol.45 , pp. 1873
    • Gavrilov, S.P.1    Gitman, D.M.2    Smirnov, A.A.3
  • 26
    • 0001445898 scopus 로고
    • Euclidean functional integral approach for disorder variables and kinks
    • 0550-3213 10.1016/0550-3213(82)90523-5.
    • Marino, E. C., Schroer, B., and Swieca, J. A., " Euclidean functional integral approach for disorder variables and kinks.," Nucl. Phys. B 0550-3213 10.1016/0550-3213(82)90523-5 200, 473 (1982).
    • (1982) Nucl. Phys. B , vol.200 , pp. 473
    • Marino, E.C.1    Schroer, B.2    Swieca, J.A.3
  • 27
    • 0000115998 scopus 로고
    • The order/disorder quantum field operators associated with the two-dimensional Ising model in the continuum limit
    • 0550-3213 10.1016/0550-3213(78)90499-6.
    • Schroer, B. and Truong, T. T., " The order/disorder quantum field operators associated with the two-dimensional Ising model in the continuum limit.," Nucl. Phys. B 0550-3213 10.1016/0550-3213(78)90499-6 144, 80 (1978).
    • (1978) Nucl. Phys. B , vol.144 , pp. 80
    • Schroer, B.1    Truong, T.T.2
  • 28
    • 0036350608 scopus 로고    scopus 로고
    • The elliptic representation of the general Painleve VI equation
    • 0010-3640 10.1002/cpa.10045, (); e-print arXiv:math.CV/0108073.
    • Guzzetti, D., " The elliptic representation of the general Painleve VI equation.," Commun. Pure Appl. Math. 0010-3640 10.1002/cpa.10045 55, 1280 (2002); e-print arXiv:math.CV/0108073.
    • (2002) Commun. Pure Appl. Math. , vol.55 , pp. 1280
    • Guzzetti, D.1
  • 29
    • 0000254490 scopus 로고
    • Monodromy problem and the boundary condition for some Painlev́ equations
    • 0034-5318 10.2977/prims/1195183300.
    • Jimbo, M., " Monodromy problem and the boundary condition for some Painlev́ equations.," Publ. Res. Inst. Math. Sci. 0034-5318 10.2977/prims/1195183300 18, 1137 (1982).
    • (1982) Publ. Res. Inst. Math. Sci. , vol.18 , pp. 1137
    • Jimbo, M.1
  • 30
    • 0034349066 scopus 로고    scopus 로고
    • Monodromy of certain Painleve-VI transcendents and reflection groups
    • 0020-9910 10.1007/PL00005790, (); e-print arXiv:math.AG/9806056.
    • Dubrovin, B. and M. Mazzocco, " Monodromy of certain Painleve-VI transcendents and reflection groups.," Invent. Math. 0020-9910 10.1007/PL00005790 141, 55 (2000); e-print arXiv:math.AG/9806056.
    • (2000) Invent. Math. , vol.141 , pp. 55
    • Dubrovin, B.1    Mazzocco, M.2
  • 31
    • 0142005689 scopus 로고    scopus 로고
    • On the critical behavior, the connection problem and the elliptic representation of a Painlev́ VI equation
    • 1385-0172 10.1023/A:1014265919008.
    • Guzzetti, D., " On the critical behavior, the connection problem and the elliptic representation of a Painlev́ VI equation.," Math. Phys., Anal. Geom. 1385-0172 10.1023/A:1014265919008 4, 293 (2001).
    • (2001) Math. Phys., Anal. Geom. , vol.4 , pp. 293
    • Guzzetti, D.1
  • 32
    • 0000287328 scopus 로고
    • Asymptotics of a τ -function arising in the two-dimensional Ising model
    • 0010-3616 10.1007/BF02102065.
    • Tracy, C. A., " Asymptotics of a τ -function arising in the two-dimensional Ising model.," Commun. Math. Phys. 0010-3616 10.1007/BF02102065 142, 297 (1991).
    • (1991) Commun. Math. Phys. , vol.142 , pp. 297
    • Tracy, C.A.1
  • 33
    • 0031548107 scopus 로고    scopus 로고
    • Exact expectation values of local fields in the quantum sine-Gordon model
    • 0550-3213 10.1016/S0550-3213(97)00123-5, (); e-print arXiv:hep-th/ 9611238.
    • Lukyanov, S. and Zamolodchikov, A., " Exact expectation values of local fields in the quantum sine-Gordon model.," Nucl. Phys. B 0550-3213 10.1016/S0550-3213(97)00123-5 493, 571 (1997); e-print arXiv:hep-th/9611238.
    • (1997) Nucl. Phys. B , vol.493 , pp. 571
    • Lukyanov, S.1    Zamolodchikov, A.2
  • 34
    • 0036329601 scopus 로고    scopus 로고
    • Fredholm determinants, Jimbo-Miwa-Ueno tau-functions, and representation theory
    • 0010-3640 10.1002/cpa.10042, (); e-print arXiv:math-ph/0111007.
    • Borodin, A. and Deift, P., " Fredholm determinants, Jimbo-Miwa-Ueno tau-functions, and representation theory.," Commun. Pure Appl. Math. 0010-3640 10.1002/cpa.10042 55, 1160 (2002); e-print arXiv:math-ph/0111007.
    • (2002) Commun. Pure Appl. Math. , vol.55 , pp. 1160
    • Borodin, A.1    Deift, P.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.