Heat kernel for higher-order differential operators in Euclidean space

2018/12/29 by Wachowski, W., Pronin, P. I. · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1812.11399

Abstract

We consider heat kernel for higher-order operators with constant coefficients in d-dimensio\-nal Euclidean space and its asymptotic behavior. For arbitrary operators which are invariant with respect to O(d)-rotations we obtain exact analytical expressions for the heat kernel and Green functions in the form of infinite series in Fox--Wright psi functions and Fox H-functions. We investigate integro-differential relations and the asymptotic behavior of the functions E_{ν, α}(z), in terms of which the heat kernel of O(d)-invariant operators are expressed. It is shown that the obtained expressions are well defined for non-integer values of space dimension d, as well as for operators of non-integer order. Possible applications of the obtained results in quantum field theory and the connection with fractional calculus are discussed.

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