Heat trace asymptotics on noncommutative spaces

Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

Volumn 3, Issue , 2007, Pages

  Vassilevich, Dmitri V ^a,b  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

Heat trace asymptotics; Noncommutative field theory

Indexed keywords

EID: 84889235551     PISSN: None     EISSN: 18150659     Source Type: Journal    
DOI: 10.3842/SIGMA.2007.093     Document Type: Article

References (48)

1. Alvarez-Gaume L., Della Pietra S., Moore G.W., Anomalies and odd dimensions, Annals Phys. 163 (1985), 288-317.
2. Avramidi I.G., Dirac operator in matrix geometry, Int. J. Geom. Methods Mod. Phys. 2 (2005), 227-264, math-ph/0502001.
3. Avramidi I., Branson T., Heat kernel asymptotics of operators with nonLaplace principal part, Rev. Math. Phys. 13 (2001), 847-890, math-ph/9905001.
4. Barvinsky A.O., Vilkovisky G.A., Covariant perturbation theory. 2. Second order in the curvature. General algorithms, Nuclear Phys. B 333 (1990), 471-511.
5. Branson T.P., Gilkey P.B., The asymptotics of the Laplacian on a manifold with boundary, Comm. Partial Differential Equations 15 (1990), 245-272.
6. Branson T.P., Gilkey P.B., Vassilevich D.V., The asymptotics of the Laplacian on a manifold with boundary. 2, Boll. Union. Mat. Ital. 11B (1997), 39-67, hep-th/9504029.
7. Branson T.P., Gilkey P.B., Kirsten K., Vassilevich D.V., Heat kernel asymptotics with mixed boundary conditions, Nuclear Phys. B 563 (1999), 603-626, hep-th/9906144.
8. Chamseddine A.H., Connes A., The spectral action principle, Comm. Math. Phys. 186 (1997), 731-750, hep-th/9606001.
9. Chamseddine A.H., Connes A., A dress for SM the beggar, arXiv:0706.3690.
10. Chu C.S., Induced Chern-Simons and WZW action in noncommutative spacetime, Nuclear Phys. B 580 (2000), 352-362, hep-th/0003007.
11. Connes A., C-algèbres et géométrie diff́erentielle, C.R. Acad. Sci. Paris 290 (1980), 599-604.
12. Connes A., Noncommutative geometry, Academic Press, London and San Diego, 1994.
13. Connes A., Landi G., Noncommutative manifolds, the instanton algebra and isospectral deformations, Comm. Math. Phys. 221 (2001), 141-159, math.QA/0011194.
14. Connes A., Dubois-Violette M., Noncommutative finite-dimensional manifolds. I. Spherical manifolds and related examples, Comm. Math. Phys. 230 (2002), 539-579, math.QA/0107070.
15. Deser S., Griguolo L., Seminara D., Gauge invariance, finite temperature and parity anomaly in D = 3, Phys. Rev. Lett. 79 (1997), 1976-1979, hep-th/9705052.
16. Dowker J.S., Critchley R., Effective Lagrangian and energy momentum tensor in de Sitter space, Phys. Rev. D 13 (1976), 3224-3232.
17. Essouabri D., Iochum B., Levy C., Sitarz A., Spectral action on noncommutative torus, arXiv:0704.0564.
18. Gayral V., Heat-kernel approach to UV/IR mixing on isospectral deformation manifolds, Ann. Henri Poincaré 6 (2005), 991-1023, hep-th/0412233.
19. Gayral V., Gracia-Bondia J.M., Ruiz F.R., Trouble with space-like noncommutative field theory, Phys. Lett. B 610 (2005), 141-146, hep-th/0412235.
20. Gayral V., Gracia-Bondia J.M., Ruiz F.R., Position-dependent noncommutative products: classical construction and field theory, Nuclear Phys. B 727 (2005), 513-536, hep-th/0504022.
21. Gayral V., Iochum B., The spectral action for Moyal plane, J. Math. Phys. 46 (2005), 043503, 17 pages, hep-th/0402147.
22. Gayral V., Iochum B., Varilly J.C., Dixmier traces on noncompact isospectral deformations, J. Funct. Anal. 237 (2006), 507-539, hep-th/0507206.
23. Gayral V., Iochum B., Vassilevich D.V., Heat kernel and number theory on NC-torus, Comm. Math. Phys. 273 (2007), 415-443, hep-th/0607078.
24. Gilkey P.B., Invariance theory, the heat equation, and the Atiyah-Singer index theorem, CRC Press, Boca Raton, FL, 1995.
25. Gilkey P.B., Asymptotic formulae in spectral geometry, Chapman & Hall/CRC, Boca Raton, FL, 2004.
26. Grandi N.E., Silva G.A., Chern-Simons action in noncommutative space, Phys. Lett. B 507 (2001), 345-350, hep-th/0010113.
27. Grosse H., Wohlgenannt M., Noncommutative QFT and renormalization, J. Phys. Conf. Ser. 53 (2006), 764-792, hep-th/0607208.
28. Grosse H., Wohlgenannt M., Induced gauge theory on a noncommutative space, hep-th/0703169.
29. Grosse H., Wulkenhaar R., Renormalisation of φ4 theory on noncommutative R4 in the matrix base, Comm. Math. Phys. 256 (2005), 305-374, hep-th/0401128.
30. Hawking S.W., Zeta function regularization of path integrals in curved space-time, Comm. Math. Phys. 55 (1977), 133-148.
31. Kirsten K., The a5 heat kernel coefficient on a manifold with boundary, Classical Quantum Gravity 15 (1998), L5-L12, hep-th/9708081.
32. Kirsten, K., Spectral functions in mathematics and physics, Chapman & Hall/CRC, Boca Raton, FL, 2001.
33. Kontsevich M., Deformation quantization of Poisson manifolds, I, Lett. Math. Phys. 66 (2003), 157-216, q-alg/9709040.
34. Madore J., The fuzzy sphere, Classical Quantum Gravity 9 (1992), 69-88.
35. Nest R., Vogt E., Werner W., Spectral action and the Connes-Chamsedinne model, Lect. Notes Phys. 596 (2002), 109-132.
36. Niemi A.J., Topological terms induced by finite temperature and density fluctuations, Phys. Rev. Lett. 57 (1986), 1102-1105.
37. Sasakura N., Heat kernel coefficients for compact fuzzy spaces, JHEP 2004 (2004), no. 12, 009, 9 pages, hep-th/0411029.
38. Sasakura, N., Effective local geometric quantities in fuzzy spaces from heat kernel expansions, JHEP 2005 (2005), no. 3, 015, 26 pages, hep-th/0502129.
39. Strelchenko A., Heat kernel of non-minimal gauge field kinetic operators on Moyal plane, Internat. J. Modern Phys. A 22 (2007), 181-202, hep-th/0608134.
40. Strelchenko A.V., Vassilevich D.V., On space-time noncommutative theories at finite temperature, Phys. Rev. D 76 (2007), 065014, 12 pages, arXiv:0705.4294.
41. Szabo R.J., Symmetry, gravity and noncommutativity, Classical Quantum Gravity 23 (2006), R199-R242, hep-th/0606233.
42. Vassilevich D.V., Vector fields on a disk with mixed boundary conditions, J. Math. Phys. 36 (1995), 3174-3182, gr-qc/9404052.
43. Vassilevich D.V., Heat kernel expansion: user's manual, Phys. Rep. 388 (2003), 279-360, hep-th/0306138.
44. Vassilevich D.V., Non-commutative heat kernel, Lett. Math. Phys. 67 (2004), 185-194, hep-th/0310144.
45. Vassilevich D.V., Spectral problems from quantum field theory, Contemp. Math. 366 (2005), 3-22, math-ph/0403052.
46. Vassilevich D.V., Quantum noncommutative gravity in two dimensions, Nuclear Phys. B 715 (2005), 695-712, hep-th/0406163.
47. Vassilevich D.V., Heat kernel, effective action and anomalies in noncommutative theories, JHEP 2005 (2005), no. 8, 085, 19 pages, hep-th/0507123.
48. Vassilevich D.V., Induced Chern-Simons action on noncommutative torus, Modern Phys. Lett. A 22 (2007), 1255-1263, hep-th/0701017.