Renormalized Path Integral in Quantum Mechanics

TL;DR

This paper develops a finite, renormalized path integral formulation of quantum mechanics that avoids ultraviolet divergences by modifying the Wiener measure, introducing an unusual diffusion process with particle sticking.

Contribution

It presents a novel, cutoff-free path integral approach with a modified measure, providing a new perspective on renormalization in quantum mechanics.

Findings

Finite, renormalized descriptions without ultraviolet cutoffs.

Modified Wiener measure describing particle sticking.

Path integral and Hamiltonian formulations are equivalent.

Abstract

We obtain direct, finite, descriptions of a renormalized quantum mechanical system with no reference to ultraviolet cutoffs and running coupling constants, in both the Hamiltonian and path integral pictures. The path integral description requires a modification to the Wiener measure on continuous paths that describes an unusual diffusion process wherein colliding particles occasionally stick together for a random interval of time before going their separate ways.