A direct approach to quantum tunneling

TL;DR

This paper introduces a direct method for calculating quantum tunneling decay rates from the Minkowski path integral, avoiding unphysical potential deformations and providing a clearer, more precise approach applicable to quantum mechanics and field theory.

Contribution

It presents a novel, direct derivation of decay rates from the Minkowski path integral, bypassing traditional instanton methods and their reliance on potential deformations.

Findings

Provides a formula for decay rates directly from Minkowski path integrals.

Enables non-perturbative and more precise calculations of tunneling phenomena.

Simplifies the conceptual understanding of quantum tunneling processes.

Abstract

The decay rates of quasistable states in quantum field theories are usually calculated using instanton methods. Standard derivations of these methods rely in a crucial way upon deformations and analytic continuations of the physical potential, and on the saddle point approximation. While the resulting procedure can be checked against other semi-classical approaches in some one-dimensional cases, it is challenging to trace the role of the relevant physical scales, and any intuitive handle on the precision of the approximations involved are at best obscure. In this paper, we use a physical definition of the tunneling probability to derive a formula for the decay rate in both quantum mechanics and quantum field theory directly from the Minkowski path integral, without reference to unphysical deformations of the potential. There are numerous benefits to this approach, from non-perturbative applications to precision calculations and aesthetic simplicity.