Path integral for half-binding potentials as quantum mechanical analog for black hole partition functions

TL;DR

This paper demonstrates that adding a Hamilton-Jacobi counterterm resolves the semi-classical approximation issues in black hole partition functions, with an analogous solution in quantum mechanics for half-binding potentials.

Contribution

It introduces a novel analogy between black hole thermodynamics and quantum mechanics, showing how Hamilton-Jacobi counterterms address unbounded actions.

Findings

Counterterms fix unbounded classical actions

Analogies between black holes and quantum mechanics are established

Improved semi-classical approximation methods

Abstract

The semi-classical approximation to black hole partition functions is not well-defined, because the classical action is unbounded and the first variation of the uncorrected action does not vanish for all variations preserving the boundary conditions. Both problems can be solved by adding a Hamilton-Jacobi counterterm. I show that the same problem and solution arises in quantum mechanics for half-binding potentials.