Gelfand-Yaglom formula for functional determinants in higher dimensions
arXiv:1808.02807 · doi:10.1088/1751-8121/aae8a7
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.
13 pages