On path integrals for wave functions taking p -adic values

Source 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 Ψ(x), defined as a map from a domain in Cp to Cp. Unlike the standard p-adic quantum mechanics formulated for functions Qp→C, our construction works directly on Cp-valued wave functions. Using p-adic Dirac delta measures and p-adic additive characters, we define the propagator as a finite-partition multiple integral, which allows explicit iterative integration. As an application, we compute the Feynman propagator for free particles and obtain a closed-form expression analogous to the classical counterpart. Our method provides a discrete, constructive alternative that complements the existing distribution-theoretic frameworks for p-adic functional integration.