Non-trivial bundles and Algebraic Classical Field Theory

TL;DR

This paper extends algebraic classical field theory to non-trivial fiber bundles, defining observables and Peierls brackets to analyze field dynamics in a more general geometric setting.

Contribution

It introduces a generalized algebraic framework for classical field theory on non-trivial bundles, incorporating Peierls brackets and causal propagators.

Findings

Formalism accommodates non-trivial fiber bundles

Defines observables as smooth functions on sections

Compares new approach with traditional methods

Abstract

Inspired by the recent algebraic approach to classical field theory, we propose a more general setting based on the manifold of smooth sections of a non-trivial fiber bundle. Central is the notion of observables over such sections, i.e. appropriate smooth functions on them. The kinematic will be further specified by means of the Peierls brackets, which in turn are defined via the causal propagators of linearized field equations. We shall compare the formalism we use with the more traditional ones.