×
Barvinsky, A. O.; Gusev, Yu. V.; Vilkovisky, G. A.; Zhytnikov, V. V.

Asymptotic behaviors of the heat kernel in covariant perturbation theory. (English) Zbl 0809.53075

J. Math. Phys. 35, No. 7, 3543-3559 (1994).
Summary: The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of \(n\)th order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the curvature inclusive. The early-time and late-time asymptotic behaviors of the trace of the heat kernel are presented with this accuracy. The late-time behavior gives the criterion of analyticity of the effective action in quantum field theory. The latter point is exemplified by deriving the effective action in two dimensions.

Cited in 20 Documents

MSC:

53Z05 Applications of differential geometry to physics
81Q15 Perturbation theories for operators and differential equations in quantum theory

Keywords:

heat kernel; curvature invariants; asymptotic behaviors; quantum field theory
Cite Review PDF
Full Text: DOI arXiv

References:

[1] Fock V., Phys. Zeit. Soviet Un. 12 pp 404– (1937)
[2] DOI: 10.1103/PhysRev.82.664 · Zbl 0043.42201 · doi:10.1103/PhysRev.82.664
[3] DOI: 10.1016/0550-3213(73)90263-0 · doi:10.1016/0550-3213(73)90263-0
[4] DOI: 10.1016/0550-3213(73)90263-0 · doi:10.1016/0550-3213(73)90263-0
[5] DOI: 10.1016/0370-1573(85)90148-6 · doi:10.1016/0370-1573(85)90148-6
[6] DOI: 10.1016/0370-2693(81)90743-7 · doi:10.1016/0370-2693(81)90743-7
[7] DOI: 10.4153/CJM-1949-021-5 · Zbl 0041.42701 · doi:10.4153/CJM-1949-021-5
[8] DOI: 10.1090/pspum/010/0237943 · doi:10.1090/pspum/010/0237943
[9] DOI: 10.1090/pspum/010/0237943 · doi:10.1090/pspum/010/0237943
[10] DOI: 10.1090/pspum/010/0237943 · doi:10.1090/pspum/010/0237943
[11] Gilkey P. B., J. Diff. Geom. 10 pp 601– (1975)
[12] DOI: 10.1088/0305-4470/20/11/014 · doi:10.1088/0305-4470/20/11/014
[13] DOI: 10.1088/0305-4470/20/11/014 · doi:10.1088/0305-4470/20/11/014
[14] DOI: 10.1088/0305-4470/20/11/014 · doi:10.1088/0305-4470/20/11/014
[15] DOI: 10.1016/0370-1573(90)90120-Q · doi:10.1016/0370-1573(90)90120-Q
[16] DOI: 10.1063/1.529179 · Zbl 0778.58062 · doi:10.1063/1.529179
[17] DOI: 10.1063/1.529179 · Zbl 0778.58062 · doi:10.1063/1.529179
[18] DOI: 10.1016/0550-3213(87)90681-X · doi:10.1016/0550-3213(87)90681-X
[19] DOI: 10.1016/0550-3213(90)90047-H · doi:10.1016/0550-3213(90)90047-H
[20] DOI: 10.1016/0550-3213(90)90048-I · doi:10.1016/0550-3213(90)90048-I
[21] DOI: 10.1016/0370-2693(90)92105-R · doi:10.1016/0370-2693(90)92105-R
[22] DOI: 10.1016/0370-2693(90)92105-R · doi:10.1016/0370-2693(90)92105-R
[23] DOI: 10.1016/0370-2693(90)92105-R · doi:10.1016/0370-2693(90)92105-R
[24] DOI: 10.1016/0370-2693(82)90520-2 · doi:10.1016/0370-2693(82)90520-2
[25] DOI: 10.1016/0370-2693(82)90520-2 · doi:10.1016/0370-2693(82)90520-2
[26] DOI: 10.1103/PhysRevA.24.2187 · doi:10.1103/PhysRevA.24.2187
[27] DOI: 10.1103/PhysRevA.24.2187 · doi:10.1103/PhysRevA.24.2187
[28] DOI: 10.1103/PhysRevA.24.2187 · doi:10.1103/PhysRevA.24.2187
[29] DOI: 10.1016/0370-2693(90)90380-O · doi:10.1016/0370-2693(90)90380-O
[30] DOI: 10.1016/0370-2693(90)90380-O · doi:10.1016/0370-2693(90)90380-O
[31] DOI: 10.1007/BF02345020 · Zbl 1378.83040 · doi:10.1007/BF02345020
[32] DOI: 10.1016/0370-2693(81)90542-6 · doi:10.1016/0370-2693(81)90542-6
[33] DOI: 10.1088/0264-9381/9/4/008 · doi:10.1088/0264-9381/9/4/008
[34] DOI: 10.1016/0370-2693(93)91365-T · doi:10.1016/0370-2693(93)91365-T
[35] DOI: 10.1063/1.530427 · Zbl 0809.53085 · doi:10.1063/1.530427
[36] DOI: 10.1088/0264-9381/9/2/006 · Zbl 0748.58037 · doi:10.1088/0264-9381/9/2/006
[37] DOI: 10.1016/0370-2693(91)90300-F · doi:10.1016/0370-2693(91)90300-F
[38] DOI: 10.1016/0370-2693(92)90550-N · doi:10.1016/0370-2693(92)90550-N
[39] DOI: 10.1103/PhysRevD.31.2439 · doi:10.1103/PhysRevD.31.2439
[40] DOI: 10.1016/0370-2693(77)90759-6 · doi:10.1016/0370-2693(77)90759-6
[41] DOI: 10.1016/0370-2693(77)90759-6 · doi:10.1016/0370-2693(77)90759-6
[42] DOI: 10.1016/0370-2693(77)90759-6 · doi:10.1016/0370-2693(77)90759-6
[43] DOI: 10.1007/BF02746592 · doi:10.1007/BF02746592
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.