Time and Observables in Covariant Quantum Theory

TL;DR

This paper proposes a modified covariant quantum theory where proper time gains a dynamic role, aligning quantum change with classical laws, and applies it to relativistic particles and cosmological models.

Contribution

It introduces a new formalism that incorporates proper time as a dynamic variable in covariant quantum theory, aligning quantum and classical evolution.

Findings

Proper time becomes a dynamic quantity in the modified formalism.

Application to relativistic scalar particles shows consistent quantum evolution.

Homogeneous cosmological model demonstrates the formalism's applicability.

Abstract

A modification of the covariant theory is proposed in which the self-energy of the system, corresponding to time-like degrees of freedom in the configuration space, preserves the classical law of change in quantum theory. As a result, proper time in covariant quantum theory takes on a dynamic meaning. As applications of the new formalism, a modification of the relativistic quantum mechanics of a scalar particle and a homogeneous model of the universe is considered.