Closed Path Integrals and Renormalisation in Quantum Mechanics

TL;DR

This paper proposes a closed-form expression for quantum transition path integrals, introduces a renormalized quantum action, and provides numerical results for a quartic potential, with implications for quantum chaos and instantons.

Contribution

It introduces a novel closed-form expression for path integrals and a renormalized quantum action, advancing analytical and numerical methods in quantum mechanics.

Findings

Derived a closed-form path integral expression.

Presented numerical results for quartic potential.

Highlighted relevance for quantum chaos and instantons.

Abstract

We suggest a closed form expression for the path integral of quantum transition amplitudes. We introduce a quantum action with renormalized parameters. We present numerical results for the $V \sim x^{4}$ potential. The renormalized action is relevant for quantum chaos and quantum instantons.