On p-Adic Functional Integration

TL;DR

This paper explores p-adic generalizations of Feynman path integrals in quantum mechanics, demonstrating that p-adic path integrals resemble their real counterparts and calculating the probability amplitude for a particle in a constant field.

Contribution

It introduces a p-adic formulation of path integrals, showing their structural similarity to real-space integrals and providing explicit calculations for specific quantum systems.

Findings

p-adic path integrals have the same form as real path integrals

Probability amplitude for a particle in a constant field is calculated in p-adic space

p-adic path integrals can be used to analyze quantum systems in p-adic frameworks

Abstract

p-Adic generalization of the Feynman path integrals in quantum mechanics is considered. The probability amplitude for a particle in a constant field is calculated. Path integrals over p-adic space have the same form as those over R.