The momentum map for nonholonomic field theories with symmetry

TL;DR

This paper generalizes the concept of the momentum map to nonholonomic field theories with symmetry and establishes a covariant momentum equation, linking field theory and mechanics through the Cauchy formalism.

Contribution

It introduces a covariant momentum map for nonholonomic field theories and demonstrates its equivalence with mechanical momentum maps via the Cauchy formalism.

Findings

Covariant nonholonomic momentum equation proved.

Momentum maps in field theories coincide with mechanical counterparts.

Framework unifies field theory and mechanics for nonholonomic systems.

Abstract

In this note, we introduce a suitable generalization of the momentum map for nonholonomic field theories and prove a covariant form of the nonholonomic momentum equation. We show that these covariant objects coincide with their counterparts in mechanics by making the transition to the Cauchy formalism.