Gelfand-Yaglom formula for functional determinants in higher dimensions

Ossipov, Alexander

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.

Citation

Ossipov, A. (2018). Gelfand-Yaglom formula for functional determinants in higher dimensions. Journal of Physics A: Mathematical and Theoretical, 51(49), Article 495201. https://doi.org/10.1088/1751-8121/aae8a7

• 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
• Contract Date: Nov 7, 2018