This book treats the Atiyah-Singer index theorem using the heat equation, which gives a
local formula for the index of any elliptic complex. Heat equation methods are also used to …

This book provides a comprehensive treatment of quantum mechanics from a mathematics
perspective and is accessible to mathematicians starting with second-year graduate …

Functional determinants of differential operators play a prominent role in theoretical and
mathematical physics, and in particular in quantum field theory. They are, however, difficult …

We present a simple and accessible method which uses contour integration methods to
derive formulae for functional determinants. To make the presentation as clear as possible …

For a closed codimension one submanifold Γ of a compact manifold M, let M Γ be the
manifold with boundary obtained by cutting M along Γ. Let A be an elliptic differential …

Simple and analytically tractable expressions for functional determinants are known to exist
for many cases of interest. We extend the range of situations for which these hold to cover …

We present a direct approach for the calculation of functional determinants of the Laplace
operator on balls. Dirichlet and Robin boundary conditions are considered. Using this …

We provide non-trivial checks of the recently proposed duality between double-scaled SYK
and a 2d dilaton gravity model with sine potential, studying the path integral at one-loop …

A bstract We study the strong coupling behaviour of 1/4-BPS circular Wilson loops (a family
of “latitudes”) in\(\mathcal {N}= 4\) Super Yang-Mills theory, computing the one-loop …

This paper, based on results obtained in recent years with various coauthors, 1–3, 13, 53
presents a proposal to extend some classical geometric concepts to a class of infinite …