p-Adic Path Integrals for Quadratic Actions

Abstract

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

9 pages