Invariance in adelic quantum mechanics

TL;DR

This paper explores the invariance properties of adelic quantum mechanics, demonstrating its symmetry under real and p-adic number field exchanges and invariance of Feynman path integrals with rational coefficients.

Contribution

It reveals the invariance of adelic quantum mechanics under field exchanges and rational coefficient transformations, highlighting its fundamental symmetries.

Findings

Adelic quantum mechanics is invariant under real and p-adic field interchange.

Feynman path integrals for quadratic actions with rational coefficients are invariant under rational transformations.

The invariance suggests deep symmetries in the mathematical structure of adelic quantum mechanics.

Abstract

Adelic quantum mechanics is form invariant under an interchange of real and p-adic number fields as well as rings of p-adic integers. We also show that in adelic quantum mechanics Feynman's path integrals for quadratic actions with rational coefficients are invariant under changes of their entries within nonzero rational numbers.