Actions, Charges and Off-Shell Fields in the Unfolded Dynamics Approach

TL;DR

This paper explores the unfolded dynamics framework, representing actions and charges via cohomology of $L_$ algebras, and formulates off-shell constraints and fundamental equations like Yang-Mills and Einstein in this setting.

Contribution

It introduces a cohomological approach to actions and charges within unfolded dynamics and provides a closed-form unfolded formulation of Yang-Mills and Einstein equations.

Findings

Actions and charges are represented as cohomology elements.

Off-shell constraints are expressed as zero curvature and covariant constancy conditions.

Unfolded formulations of Yang-Mills and Einstein equations are explicitly presented.

Abstract

Within unfolded dynamics approach, we represent actions and conserved charges as elements of cohomology of the $L_\infty$ algebra underlying the unfolded formulation of a given dynamical system. The unfolded off-shell constraints for symmetric fields of all spins in Minkowski space are shown to have the form of zero curvature and covariant constancy conditions for 1-forms and 0-forms taking values in an appropriate star product algebra. Unfolded formulation of Yang-Mills and Einstein equations is presented in a closed form.