PreprintCC BY 4.0arXiv
A nonrecursive method for computing the off-diagonal small-time heat kernel expansion
Abstract
We present a nonrecursive method to compute the small-time heat kernel asymptotic expansion. The Klein-Gordon operator in flat space-time coupled to electromagnetic fields is considered. We obtain closed-form expressions for the expansion coefficients up to the second order in time. Our approach can be regarded as an extension of the method described in [R.I. Nepomechie, Phys. Rev. D 31, 3291 (1985)], but unlike that work, our approach is valid for arbitrary space-time dependence of the heat kernel, i.e. for off-diagonal values. We verify that our results correctly reproduce small-time asymptotics of the heat kernel for a plane wave field and for constant electromagnetic fields.
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BibTeX
@misc{guba2026nonrecursive,
title = {{A nonrecursive method for computing the off-diagonal small-time heat kernel expansion}},
author = {Vyacheslav O. Guba and Alexey V. Reznichenko},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10640},
eprint = {2609.10640},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10640},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A nonrecursive method for computing the off-diagonal small-time heat kernel expansion
AU - Vyacheslav O. Guba
AU - Alexey V. Reznichenko
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10640
UR - https://arxiv.org/abs/2609.10640
AB - We present a nonrecursive method to compute the small-time heat kernel asymptotic expansion. The Klein-Gordon operator in flat space-time coupled to electromagnetic fields is considered. We obtain closed-form expressions for the expansion coefficients up to the second order in time. Our approach can be regarded as an extension of the method described in [R.I. Nepomechie, Phys. Rev. D 31, 3291 (1985)], but unlike that work, our approach is valid for arbitrary space-time dependence of the heat kernel, i.e. for off-diagonal values. We verify that our results correctly reproduce small-time asymptotics of the heat kernel for a plane wave field and for constant electromagnetic fields.
ER -