Nonstandard Feynman path integral for the harmonic oscillator

TL;DR

This paper rigorously computes the harmonic oscillator Feynman path integral using nonstandard analysis, revealing classical physics properties emerge naturally from quantum mechanics without prior classical path knowledge.

Contribution

It introduces a novel nonstandard analysis approach to compute the harmonic oscillator path integral without relying on classical paths.

Findings

Properties of classical physics emerge naturally from quantum calculations

Provides a rigorous nonstandard analysis framework for path integrals

Eliminates the need for classical path knowledge in computations

Abstract

we will provide a rigorous computation for the harmonic oscillator Feynman path integral. The computation will be done without having prior knowledge of the classical path. We will see that properties of classical physics falls out naturally from a purely quantum mechanical point of view. We will assume that the reader is familiar with Nonstandard Analysis.