Gelfand-Yaglom formula for functional determinants in higher dimensions
Mathematical Physics
2018-11-16 v2 Statistical Mechanics
High Energy Physics - Theory
math.MP
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.
Cite
@article{arxiv.1808.02807,
title = {Gelfand-Yaglom formula for functional determinants in higher dimensions},
author = {A. Ossipov},
journal= {arXiv preprint arXiv:1808.02807},
year = {2018}
}
Comments
13 pages