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.

arXiv:2609.10640 [quant-ph]

(or arXiv:2609.10640v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.10640 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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