Classicalization and Quantization of Tachyon-like Matter on (non)Archimedean Spaces

TL;DR

This paper explores classical and quantum models of tachyon-like scalar fields inspired by string theory, considering both real and p-adic number spaces, and discusses their propagators and potential adelic generalizations.

Contribution

It introduces a framework for analyzing tachyon-like fields over nonarchimedean spaces and computes their quantum propagators, extending the understanding of such fields in cosmological contexts.

Findings

Canonical transformations simplify equations of motion.

Quantum propagators are explicitly calculated for real and p-adic spaces.

Potential for a quantum adelic generalization is discussed.

Abstract

We consider a class of tachyon-like potentials, inspired by string theory, D-brane dynamics and cosmology in the context of classical and quantum mechanics. Motivated by the trans-Plankcian problem in the very early stage of cosmological evolution of the Universe, we consider the theoretical role of DBI-type tachyon scalar field, defined over the field of real as well as $p$-adic numbers, i.e. archemedean and nonarchimedean spaces. To simplify the equation of motion for the scalar field, canonical transformations are defined and engaged. The corresponding quantum propagators in the Feynman path integral approach on real and nonarchimedean spaces are calculated and discussed, as are possibilities for a quantum adelic generalization and its application.