Spectral Action for Torsion with and without Boundaries

Communications in Mathematical Physics

Volumn 310, Issue 2, 2012, Pages 367-382

  Iochum, B ^a,b   Levy, C ^c   Vassilevich, D ^d,e  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

^b AIX MARSEILLE UNIVERSITY   (France)

^c UNIVERSITY OF COPENHAGEN   (Denmark)

^d UNIVERSIDADE FEDERAL DO ABC   (Brazil)

^e ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84857233711     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-011-1406-7     Document Type: Article

References (39)

1. Andrianov A. A., Lizzi F.: Bosonic spectral action induced from anomaly cancellation. JHEP 1005, 057 (2010).
2. Beneventano C., Gilkey P., Kirsten K., Santangelo E.: Strong ellipticity and spectral properties of chiral bag boundary conditions. J. Phys. A: Math. Gen. 36, 11533-11543 (2003).
3. Branson T. P., Gilkey P. B.: The asymptotics of the Laplacian on a manifold with boundary. Commun. Part. Diff. Eq. 15, 245-272 (1990).
4. Branson T., Gilkey P.: Residues of the eta function for an operator of Dirac type with local boundary conditions. Diff. Geom. Appl. 2, 249-267 (1992).
5. Branson T., Gilkey P., Kirsten K., Vassilevich D.: Heat kernel asymptotics with mixed boundary conditions. Nucl. Phys. B 563, 603-626 (1999).
6. Chamseddine A., Connes A.: The spectral action principle. Commun. Math. Phys. 186, 731-750 (1997).
7. Chamseddine A., Connes A.: Quantum gravity boundary terms from the spectral action on noncommutative space. PRL 99, 071302 (2007).
8. Chamseddine A., Connes A.: Noncommutative geometric spaces with boundary: spectral action. J. Geom. Phys. 61, 317-332 (2011).
9. Chamseddine A., Connes A., Marcolli M.: Gravity and the standard model with neutrino mixing. Adv. Theor. Math. Phys. 11, 991-1089 (2007).
10. Cognola G., Zerbini S.: Heat kernel expansion in geometric fields. Phys. Lett. B 195, 435-438 (1987).
11. Connes A.: Noncommutative Geometry. Academic Press, London-San Diego (1994).
12. Connes, A., Marcolli, M.: Noncommutative Geometry, Quantum Fields and Motives. Colloquium Publications, Vol. 55, Providence. RI: Amer. Math. Soc., 2008.
13. Eguchi T., Gilkey P. B., Hanson A. J.: Gravitation, gauge theories and differential geometry. Phys. Rept. 66, 213-393 (1980).
14. Esposito G., Gilkey P., Kirsten K.: Heat kernel coefficients for chiral bag boundary conditions. J. Phys. A: Math. Gen. 38, 2259-2276 (2005).
15. Esposito G., Kirsten K.: Chiral bag boundary conditions on the ball. Phys. Rev. D 66, 085014 (2002).
16. Friedrich, Th., Sulanke, S.: Ein kriterium für die formale selbstadjungiertheit des Dirac-operators. Coll. Math. XL, 239-247 (1979).
17. Gilkey, P. B.: Invariance Theory, the heat equation, and the Atiyah-Singer Index theorem. Mathematics Lecture Series, Vol. 11, Wilmington, DE: Publish or Perish, Inc., 1984.
18. Gilkey, P. B.: Asymptotic Formulae in Spectral Geometry. Boca Raton, FL: Chapman & Hall/CRC, 2004.
19. Gilkey P., Kirsten K.: Stability theorems for chiral bag boundary conditions. Lett. Math. Phys. 73, 147-163 (2005).
20. Goldthorpe W. H.: Spectral geometry and SO(4) gravity in a Riemann-Cartan spacetime. Nucl. Phys. B 170, 307-328 (1980).
21. Grensing G.: Induced gravity for nonzero torsion. Phys. Lett. 169, 333-336 (1986).
22. Grubb, G.: Functional calculus of pseudodifferential boundary problems. Second edition, Progress in Mathematics 65, Boston: Birkhäuser, 1996.
23. Hanish F., Pfäffle F., Stephan C. A.: The spectral action for Dirac operators with skew-symmetric torsion. Commun. Math. Phys. 300, 877-888 (2010).
24. Hasenfratz P., Kuti J.: The quark bag model. Phys. Rept. 40, 75-179 (1978).
25. Hawking S., Horowitz G.: The gravitational Hamiltonian, action, entropy and surface terms. Class. Quantum Grav. 13, 1487-1498 (1996).
26. Heckel B. R., Adelberger E. G., Cramer C. E., Cook T. S., Schlamminger S., Schmidt U.: Preferred-frame and CP-violation tests with polarized electrons. Phys. Rev. D 78, 092006 (2008).
27. 2. Nucl. Phys. B 245, 118-126 (1984).
28. Iochum B., Levy C.: Tadpoles and commutative spectral triples. J. Noncommut. Geom. 5, 299-329 (2011).
29. Iochum B., Levy C.: Spectral triples and manifolds with boundary. J. Funct. Anal. 260, 117-134 (2011).
30. Kirsten, K.: Spectral Functions in Mathematics and Physics. Boca Ratonm, FL: Chapman & Hall/CRC, 2002.
31. Kleinert H.: New gauge symmetry in gravity and the evanescent role of torsion. Electron. J. Theor. phys. 27, 287 (2010).
32. Kostelecky V. A., Russell N., Tasson J.: Constraints on torsion from Lorentz violation. Phys. Rev. Lett. 100, 111102 (2008).
33. Marachevsky V. N., Vassilevich D. V.: Chiral anomaly for local boundary conditions. Nucl. Phys. B 677, 535-552 (2004).
34. Obukhov Y. N.: Spectral geometry of the Riemann-Cartan space-time. Nucl. Phys. B 212, 237-254 (1983).
35. Shapiro I. L.: Physical aspects of the space-time torsion. Phys. Rept. 357, 113-213 (2002).
36. th Meeting on CPT and oreatz Symmetry (Bloomington. IN, five 28-July 2, 2010).
37. Vassilevich D. V.: Vector fields on a disk with mixed boundary conditions. J. Math. Phys. 36, 3174-3182 (1995).
38. Vassilevich D. V.: Heat kernel expansion: user's manual. Phys. Rep. 388, 279-360 (2003).
39. Wipf A., Dürr S.: Gauge theories in a bag. Nucl. Phys. B 443, 201-232 (1995).