On p-adic path integral

TL;DR

This paper extends Feynman's path integral formulation to p-adic quantum mechanics, analytically evaluating it for quadratic Lagrangians and showing it has a similar form to the real case.

Contribution

It introduces a p-adic path integral framework and provides an explicit analytical evaluation for quadratic Lagrangians, bridging p-adic and real quantum mechanics.

Findings

p-adic path integral has the same form as in ordinary quantum mechanics

Analytical evaluation achieved for quadratic Lagrangians

Supports the consistency of p-adic quantum mechanics with classical results

Abstract

Feynman's path integral is generalized to quantum mechanics on p-adic space and time. Such p-adic path integral is analytically evaluated for quadratic Lagrangians. Obtained result has the same form as that one in ordinary quantum mechanics.