Quantum Geometry of a Configuration Space in a Covariant Dynamical Theory

TL;DR

This paper develops a quantum action principle for a covariant two-particle system, introducing a quantum geometry in configuration space that generalizes classical notions and aids in observable generation.

Contribution

It formulates a quantum action principle for a covariant dynamical theory, defining a quantum geometry via eigenvalues of the quantum action.

Findings

Quantum action eigenvalues define a quantum geometry.

The framework allows generation of observables with probe fields.

Provides a covariant quantum theory for relativistic particles.

Abstract

A quantum version of the action principle in a simple covariant dynamical theory of two relativistic particles is formulated. The central object of this new formulation of quantum theory is a stationary eigenvalue of the quantum action. This quantity defines a quantum geometry in a configuration space. In the presence of "probe" fields it plays the role of a generation function of observables.