Spectral invariants for the Dirac equation on the d-ball with various boundary conditions

Classical and Quantum Gravity

Volumn 13, Issue 11, 1996, Pages 2911-2920

  Dowker, J S ^a   Apps, J S ^a   Kirsten, K ^b   Bordag, M ^b  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

^b UNIVERSITY OF LEIPZIG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22244466394     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/13/11/007     Document Type: Article

References (51)

1. Atiyah M F, Patodi V K and Singer I M 1975 Spectral asymmetry and Riemannian geometry Math. Proc. Camb. Phil. Soc. 77 43
2. Awada M A and Toms D J 1984 Induced gravitational and gauge-field actions from quantised matter fields in non-abelian Kaluza-Klein theory Nucl. Phys. B 245 161
3. Baacke J and Igarishi Y 1983 Casimir energy of confined massive quarks Phys. Rev. D 27 460
4. Baltes H P and Hilf E M 1976 Spectra of Finite Systems (Mannheim: Bibligraphisches Institut)
5. Barvinsky A O, Kamenshchik Yu A and Karmazin I P 1992 One-loop quantum cosmology Ann. Phys. 219 201
6. Bender C M and Hays P 1976 Zero point energy of fields in a confined volume Phys. Rev. D 14 2622
7. Bordag M, Elizalde E and Kirsten K 1996 Heat kernel coefficients of the Laplace operator on the D-dimensional ball J. Math. Phys. 37 895
8. Bordag M, Geyer B, Kirsten K and Elizalde E 1996 Zeta function determinant of the Laplace operator on the D-dimensional ball Commun. Math. Phys. 179 215
9. Branson T P and Gilkey P B 1990 Commun. Partial Diff. Eqns 15 245
10. Branson T P, Gilkey P B and Vassilevich D V 1996 The asymptotics of the Laplacian on a manifold with boundary II Preprint hep-th/9504029
11. Camporesi R and Higuchi A 1996 On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces J. Geom. Phys. 15 1
12. Cognola G and Kirsten K 1996 Class. Quantum Grav. 13 633
13. D'Eath P D and Halliwell J J 1987 Fermions in quantum cosmology Phys. Rev. D 35 1100
14. D'Eath P D and Esposito G V M 1991 Local boundary conditions for Dirac operator and one-loop quantum cosmology Phys. Rev. D 43 3234
15. D'Eath P D and Esposito G V M 1991 Spectral boundary conditions in one-loop quantum cosmology Phys. Rev. D 44 1713
16. Dowker J S 1996 Robin conditions on the Euclidean ball Preprint MUTP/95/7; Class. Quantum Grav. 13 585
17. Dowker J S 1996 Spin on the 4-ball Phys. Lett. 366B 89
18. Dowker J S and Apps J S 1995 Functional determinants on certain domains Proc. 6th Moscow Quantum Gravity Seminar (Moscow) to appear
19. Esposito G, Kamenshchik A Y, Mishakov I V and Pollifrone G 1994 Gravitons in one-loop quantum cosmology Phys. Rev. D 50 6329;
20. 1995 Phys. Rev. D 52 3457
21. Esposito G 1994 Quantum Gravity, Quantum Cosmology and Lorentzian Geometries (Lecture Notes in Physics Monographs 12) (Berlin: Springer)
22. Esposito G 1996 Nonlocal properties in Euclidean quantum gravity Proc. 3rd Workshop on Quantum Field Theory under the Influence of External Conditions (Leipzig: Teubner)
23. Esposito G, Morales-Técotl H A and Pimentel L O 1996 Essential self-adjointness in one-loop quantum cosmology Class. Quantum Grav. 13 957
24. Forgacs P, O'Raifeartaigh L and Wipf A 1987 Scattering theory U(1) anomaly and index theorems for compact and non-compact manifolds Nucl. Phys. B 293 559
25. Gilkey P B 1995 Invariance Theory the Heat Equation and the Atiyah-Singer Index Theorem 2nd edn (Boca Raton, FL: Chemical Rubber Company)
26. Gilkey P B 1993 On the index of geometric operators for Riemannian manifolds with boundary Adv. Math. 102 129
27. Gilkey P B 1975 The boundary integrand in the formula for the signature and Euler characteristic of a manifold with boundary Adv. Math. 15 334
28. Grubb G 1992 Commun. Partial Diff. Eqns 17 2031
29. Grubb G and Seeley R T 1993 C. R. Acad. Sci. (Paris) 317 1124;
30. 1995 Invent. Math. 121 481
31. Jaroszewicz T and Kurzepa P S 1992 Polyakov spin factors and Laplacians on homogeneous spaces Ann. Phys. 213 135
32. Kamenshchik Yu A and Mishakov I V 1993 Fermions in one-loop quantum cosmology Phys. Rev. D 47 1380
33. Kamenshchik Yu A and Mishakov I V 1992 Zeta function technique for quantum cosmology Int. J. Mod. Phys. A 7 3265
34. Levitin M 1996 Dirichlet and Neumann invariants for Euclidean balls Diff. Geom. Appl. to be published
35. Luckock H C 1991 Mixed boundary conditions in quantum field theory J. Math. Phys. 32 1755
36. Luckock H C and Moss I G 1989 The quantum geometry of random surfaces and spinning strings Class. Quantum Grav. 6 1993
37. Ma Z Q 1986 Axial anomaly and index theorem for a two-dimensional disc with boundary J. Phys. A: Math. Gen. 19 L317
38. McAvity D M 1992 Heat-kernel asymptotics for mixed boundary conditions Class. Quantum Grav. 9 1983
39. Marachevsky V N and Vassilevich D V 1996 Diffeomorphism invariant eigenvalue problem for metric perturbations in abounded region SPbU-IP-95 Preprint gr-qc/9509051
40. Milton K A 1980 Zero point energy of confined fermions Phys. Rev. D 22 1444
41. Mishchenko A V and Sitenko Yu A 1992 Spectral boundary conditions and index theorem for two-dimensional manifolds with boundary Ann. Phys. 218 199
42. Moss I G 1996 Quantum Theory of Black Holes (New York: Wiley)
43. Moss I G 1989 Boundary terms in the heat-kernel expansion Class. Quantum Grav. 6 759
44. Moss I G and Poletti S J 1994 Conformal anomaly on an Einstein space with boundary Phys. Lett. 333B 326
45. Niemi A J and Semenoff G W 1986 Index theorem on open infinite manifolds Nucl. Phys. B 269 131
46. Ninomiya M and Tan C I 1985 Axial anomaly and index theorem for manifolds with boundary Nucl. Phys. B 245 199
47. 2u = 0 (Leipzig: Teubner)
48. Rayleigh 1877-8 Theory of Sound vol I, II (London: MacMillan)
49. Römer H and Schroer P B 1977 Phys. Lett. 21 182
50. Trautman A 1992 Spinors and Dirac operators on hypersurfaces J. Math. Phys. 33 4011
51. Vassilevich D V Vector fields on a disk with mixed boundary conditions Preprint gr-qc/9404052