On path integrals for wave functions taking $p$-adic values

Abstract

In this paper, we construct a $p$-adic path integral via $p$-adic multiple integrals. This integral describes the evolution of a wave function $\hat{I}¨(x)$, which is defined as a map from a domain in ${\mathbb{C}}_p$ to ${\mathbb{C}}_p$. We also compute the Feynman propagator for free particles, demonstrating that the result obtained is similar to the classical counterparts.

8 pages