Scalar heat kernel with boundary in the worldline formalism

Journal of High Energy Physics

Volumn 2008, Issue 10, 2008, Pages

  Bastianelli, Fiorenzo ^a,b   Corradini, Olindo ^b,c   Pisani, Pablo A G ^d,e   Schubert, Christian ^a,c  

^a ALBERT EINSTEIN INSTITUT   (Germany)

^b UNIVERSITY OF BOLOGNA   (Italy)

^c UNIVERSIDAD MICHOACANA DE SAN NICOLÁS DE HIDALGO   (Mexico)

^d FRIEDRICH SCHILLER UNIVERSITY JENA   (Germany)

^e UNIVERSIDAD NACIONAL DE LA PLATA   (Argentina)

Author keywords

Field theories in higher dimensions; Field theories in lower dimensions; Sigma models

Indexed keywords

EID: 58149314359     PISSN: 11266708     EISSN: 10298479     Source Type: Journal    
DOI: 10.1088/1126-6708/2008/10/095     Document Type: Article

References (54)

1. Z. Bern and D.A. Kosower, The computation of loop amplitudes in gauge theories 1992 Nucl. Phys. B 379 451
2. M.J. Strassler, Field theory without Feynman diagrams: one loop effective actions 1992 Nucl. Phys. B 385 145 [hep-ph/9205205]
3. R.D. Ball, Chiral gauge theory 1989 Phys. Rep. 182 1
4. D.V. Vassilevich, Heat kernel expansion: user's manual 2003 Phys. Rep. 388 279 [hep-th/0306138]
5. K. Kirsten, Spectral functions in mathematics and physics http://www.slac.stanford.edu/spires/find/hep/www?irn=4785843, U.S.A. (2001)
6. C. Schubert, Perturbative quantum field theory in the string-inspired formalism 2001 Phys. Rep. 355 73 [hep-th/0101036]
7. D. Fliegner, P. Haberl, M.G. Schmidt and C. Schubert, The higher derivative expansion of the effective action by the string inspired method. II 1998 Ann. Phys. (NY) 264 51 [hep-th/9707189]
8. D. Fliegner, M.G. Schmidt and C. Schubert, The higher derivative expansion of the effective action by the string inspired method. Part 1 1994 Z. Physik C 64 111 [hep-ph/9401221]
9. D. Fliegner, P. Haberl, M.G. Schmidt and C. Schubert, An improved heat kernel expansion from worldline path integrals 1995 Discourses Math. Appl. 4 87 [hep-th/9411177]
10. M.G. Schmidt and C. Schubert, On the calculation of effective actions by string methods 1993 Phys. Lett. B 318 438 [hep-th/9309055]
11. D.G.C. McKeon and T.N. Sherry, Radiative effects in a constant magnetic field using the quantum mechanical path integral 1994 Mod. Phys. Lett. A 9 2167
12. D. Cangemi, E. D'Hoker and G.V. Dunne, Derivative expansion of the effective action and vacuum instability for QED in (2+1)-dimensions 1995 Phys. Rev. D 51 2513 [hep-th/9409113]
13. V.P. Gusynin and I.A. Shovkovy, Derivative expansion for the one-loop effective Lagrangian in QED 1996 Can. J. Phys. 74 282 [hep-ph/9509383]
14. V.P. Gusynin and I.A. Shovkovy, Derivative expansion of the effective action for QED in 2+1 and 3+1 dimensions 1999 J. Math. Phys. 40 5406 [hep-th/9804143]
15. R. Shaisultanov, On the string-inspired approach to QED in external field 1996 Phys. Lett. B 378 354 [hep-th/9512142]
16. M. Reuter, M.G. Schmidt and C. Schubert, Constant external fields in gauge theory and the spin 0, 1/2, 1 path integrals 1997 Ann. Phys. (NY) 259 313 [hep-th/9610191]
17. U. Müller, Basis invariants in non-Abelian gauge theories DESY-96-154 [hep-th/9701124]
18. F. Bastianelli, The path integral for a particle in curved spaces and Weyl anomalies 1992 Nucl. Phys. B 376 113 [hep-th/9112035]
19. F. Bastianelli and P. van Nieuwenhuizen, Trace anomalies from quantum mechanics 1993 Nucl. Phys. B 389 53 [hep-th/9208059]
20. F.A. Dilkes and D.G.C. McKeon, Off-diagonal elements of the DeWitt expansion from the quantum mechanical path integral 1996 Phys. Rev. D 53 4388 [hep-th/9509005]
21. F. Bastianelli and O. Corradini, On mode regularization of the configuration space path integral in curved space 1999 Phys. Rev. D 60 044014 [hep-th/9810119]
22. F. Bastianelli and O. Corradini, 6D trace anomalies from quantum mechanical path integrals 2001 Phys. Rev. D 63 065005 [hep-th/0010118]
23. F. Bastianelli and A. Zirotti, Worldline formalism in a gravitational background 2002 Nucl. Phys. B 642 372 [hep-th/0205182]
24. F. Bastianelli, O. Corradini and A. Zirotti, Dimensional regularization for SUSY σ-models and the worldline formalism 2003 Phys. Rev. D 67 104009 [hep-th/0211134]
25. F. Bastianelli, P. Benincasa and S. Giombi, Worldline approach to vector and antisymmetric tensor fields 2005 J. High Energy Phys. JHEP04(2005)010 [hep-th/0503155]
26. F. Bastianelli, P. Benincasa and S. Giombi, Worldline approach to vector and antisymmetric tensor fields. II 2005 J. High Energy Phys. JHEP10(2005)114 [hep-th/0510010]
27. F. Bastianelli, O. Corradini and A. Zirotti, BRST treatment of zero modes for the worldline formalism in curved space 2004 J. High Energy Phys. JHEP01(2004)023 [hep-th/0312064]
28. M. Bordag, U. Mohideen and V.M. Mostepanenko, New developments in the Casimir effect 2001 Phys. Rep. 353 1 [quant-ph/0106045]
29. M. Fabinger and P. Horava, Casimir effect between world-branes in heterotic M-theory 2000 Nucl. Phys. B 580 243 [hep-th/0002073]
30. J. Garriga, O. Pujols and T. Tanaka, Radion effective potential in the brane-world 2001 Nucl. Phys. B 605 192 [hep-th/0004109]
31. S. Nojiri, S.D. Odintsov and S. Zerbini, Bulk versus boundary (gravitational Casimir) effects in quantum creation of inflationary brane world universe 2000 Class. Quantum Grav. 17 4855 [hep-th/0006115]
32. R. Hofmann, P. Kanti and M. Pospelov, (De-)stabilization of an extra dimension due to a Casimir force 2001 Phys. Rev. D 63 124020 [hep-ph/0012213]
33. H. Gies and K. Langfeld, Quantum diffusion of magnetic fields in a numerical worldline approach 2001 Nucl. Phys. B 613 353 [hep-ph/0102185]
34. H. Gies and K. Langfeld, Loops and loop clouds: a numerical approach to the worldline formalism in QED 2002 Int. J. Mod. Phys. A 17 966 [hep-ph/0112198]
35. H. Gies, K. Langfeld and L. Moyaerts, Casimir effect on the worldline 2003 J. High Energy Phys. JHEP06(2003)018 [hep-th/0303264]
36. H. Gies and K. Klingmuller, Worldline algorithms for Casimir configurations 2006 Phys. Rev. D 74 045002 [quant-ph/0605141]
37. P. Horava and E. Witten, Heterotic and type-I string dynamics from eleven dimensions 1996 Nucl. Phys. B 460 506 [hep-th/9510209]
38. P. Horava and E. Witten, Eleven-dimensional supergravity on a manifold with boundary 1996 Nucl. Phys. B 475 94 [hep-th/9603142]
39. L. lvarez-Gaumé, Supersymmetry and the Atiyah-Singer index theorem 1983 Comm. Math. Phys. 90 161
40. L. lvarez-Gaumé and E. Witten, Gravitational anomalies 1984 Nucl. Phys. B 234 269
41. D. Friedan and P. Windey, Supersymmetric derivation of the Atiyah-Singer index and the chiral anomaly 1984 Nucl. Phys. B 235 395
42. H.P. McKean and I.M. Singer, Curvature and the eigenvalues of the Laplacian 1967 J. Diff. Geom. 1 43
43. G. Kennedy, R. Critchley and J.S. Dowker, Finite temperature field theory with boundaries: stress tensor and surface action renormalization 1980 Ann. Phys. (NY) 125 346
44. T.P. Branson and P.B. Gilkey, The asymptotics of the Laplacian on a manifold with boundary 1990 Commun. Part. Diff. Equat. 15 245
45. G. Cognola, L. Vanzo and S. Zerbini, A new algorithm for asymptotic heat kernel expansion for manifolds with boundary 1990 Phys. Lett. B 241 381
46. D.M. McAvity and H. Osborn, A DeWitt expansion of the heat kernel for manifolds with a boundary 1991 Class. Quantum Grav. 8 603 [Erratum 1992 Commun. Part. Diff. Equat. 9 317]
47. D.M. McAvity and H. Osborn, Asymptotic expansion of the heat kernel for generalized boundary conditions 1991 Class. Quantum Grav. 8 1445
48. D.M. McAvity, Heat kernel asymptotics for mixed boundary conditions 1992 Class. Quantum Grav. 9 1983
49. T.P. Branson, P.B. Gilkey and D.V. Vassilevich, The asymptotics of the Laplacian on a manifold with boundary. 2 1997 Boll. Union. Mat. Ital. 11B 39 [hep-th/9504029]
50. 5 heat kernel coefficient on a manifold with boundary 1998 Class. Quantum Grav. 15 L5 [hep-th/9708081]
51. J.S. Dowker and K. Kirsten, Smeared heat-kernel coefficients on the ball and generalized cone 2001 J. Math. Phys. 42 434 [hep-th/9803094]
52. T.P. Branson, P.B. Gilkey, K. Kirsten and D.V. Vassilevich, Heat kernel asymptotics with mixed boundary conditions 1999 Nucl. Phys. B 563 603 [hep-th/9906144]
53. F. Bastianelli, O. Corradini and P.A.G. Pisani, Worldline approach to quantum field theories on flat manifolds with boundaries 2007 J. High Energy Phys. JHEP02(2007)059 [hep-th/0612236]
54. F. Bastianelli, O. Corradini and P.A.G. Pisani, Scalar field with Robin boundary conditions in the worldline formalism 2008 J. Phys. A: Math. Gen. 41 164010 [0710.4026]