p-Adic Path Integrals for Quadratic Actions

TL;DR

This paper calculates the p-adic Feynman path integral for quadratic actions, showing it matches the form in standard quantum mechanics, thus bridging p-adic and real quantum frameworks.

Contribution

It provides an exact expression for p-adic path integrals with quadratic actions, demonstrating their equivalence to those in conventional quantum mechanics.

Findings

Exact p-adic propagator matches real quantum mechanics form

Bridges p-adic and real quantum frameworks for quadratic systems

Enhances understanding of p-adic quantum mechanics

Abstract

The Feynman path integral in p-adic quantum mechanics is considered. The probability amplitude ${\cal K}_p (x^{\prime\prime},t^{\prime\prime}; x^\prime,t^\prime)$ for one-dimensional systems with quadratic actions is calculated in an exact form, which is the same as that in ordinary quantum mechanics.