A new geometric setting for classical field theories

TL;DR

This paper introduces a novel geometric framework for classical field theories, inspired by Skinner and Rusk's approach, featuring a constraint algorithm that ensures well-defined dynamics and automatically incorporates second order conditions.

Contribution

It presents a new geometric setting for classical field theories with a constraint algorithm that guarantees consistent dynamics and includes second order conditions automatically.

Findings

Developed a constraint algorithm for singular field theories.

Identified a final constraint submanifold with well-defined dynamics.

Automatically incorporates second order conditions in the geometric setting.

Abstract

A new geometrical setting for classical field theories is introduced. This description is strongly inspired in the one due to Skinner and Rusk for singular lagrangians systems. For a singular field theory a constraint algorithm is developed that gives a final constraint submanifold where a well-defined dynamics exists. The main advantage of this algorithm is that the second order condition is automatically included.