The Quantum Gauge Principle

TL;DR

This paper develops a quantum gauge principle framework for quantum fields on curved space-time, using differential geometry, and derives dynamical equations for gauge connections and scalar fields, generalizing standard equations.

Contribution

It introduces a quantum gauge principle in the context of quantum fields on curved backgrounds, extending the geometric formulation of quantum field evolution.

Findings

Derives invariant dynamical equations for quantum gauge connections and scalar fields.

Recovers standard scalar field equations in the flat bundle limit.

Provides a geometric framework for quantum field evolution on curved space-time.

Abstract

We consider the evolution of quantum fields on a classical background space-time, formulated in the language of differential geometry. Time evolution along the worldlines of observers is described by parallel transport operators in an infinite-dimensional vector bundle over the space-time manifold. The time evolution equation and the dynamical equations for the matter fields are invariant under an arbitrary local change of frames along the restriction of the bundle to the worldline of an observer, thus implementing a ``quantum gauge principle''. We derive dynamical equations for the connection and a complex scalar quantum field based on a gauge field action. In the limit of vanishing curvature of the vector bundle, we recover the standard equation of motion of a scalar field in a curved background space-time.