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Gelfand-Yaglom formula for functional determinants in higher dimensions

Ossipov, Alexander

Gelfand-Yaglom formula for functional determinants in higher dimensions Thumbnail


Authors

Alexander Ossipov



Abstract

The Gelfand–Yaglom formula relates functional determinants of the one-dimensional second order differential operators to the solutions of the corresponding initial value problem. In this work we generalise the Gelfand–Yaglom method by considering discrete and continuum partial second order differential operators in higher dimensions. To illustrate our main result we apply the generalised formula to the two-dimensional massive and massless discrete Laplace operators and calculate asymptotic expressions for their determinants.

Journal Article Type Article
Acceptance Date Oct 16, 2018
Online Publication Date Nov 7, 2018
Publication Date Dec 7, 2018
Deposit Date Nov 7, 2018
Publicly Available Date Nov 8, 2019
Journal Journal of Physics A: Mathematical and Theoretical
Print ISSN 1751-8113
Electronic ISSN 1751-8121
Publisher IOP Publishing
Peer Reviewed Peer Reviewed
Volume 51
Issue 49
Article Number 495201
DOI https://doi.org/10.1088/1751-8121/aae8a7
Keywords Modelling and simulation; Statistics and probability; Mathematical physics; General physics and astronomy; Statistical and nonlinear physics
Public URL https://nottingham-repository.worktribe.com/output/1234149
Publisher URL http://iopscience.iop.org/article/10.1088/1751-8121/aae8a7/meta
Additional Information This is an author-created, un-copyedited version of an article accepted for publication in Journal of Physics A: Mathematical and Theoretical. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://iopscience.iop.org/article/10.1088/1751-8121/aae8a7/meta

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