The Poincar\'e-Cartan Form in Superfield Theory

TL;DR

This paper provides an intrinsic geometric formulation of the Hamilton-Cartan formalism for superfield theories using the Poincaré-Cartan form, including Noether's theorem and applications in supermechanics.

Contribution

It introduces an intrinsic description of the Hamilton-Cartan formalism in superfield theory via the Poincaré-Cartan form, extending classical variational methods to supermanifolds.

Findings

Develops an intrinsic geometric framework for superfield variational problems.

Establishes a superfield version of Noether's theorem.

Provides examples from superfield theory and supermechanics.

Abstract

An intrinsic description of the Hamilton-Cartan formalism for first-order Berezinian variational problems determined by a submersion of supermanifolds is given. This is achieved by studying the associated higher-order graded variational problem through the Poincar\'e-Cartan form. Noether theorem and examples from superfield theory and supermechanics are also discussed.