TL;DR
This paper summarizes the differential calculus and cohomology on graded infinite order jet manifolds, providing a mathematical framework for Lagrangian theories involving even and odd variables using the Grassmann-graded variational bicomplex.
Contribution
It offers a comprehensive formulation of Lagrangian theories on graded jet manifolds through the Grassmann-graded variational bicomplex, advancing the mathematical foundation for such theories.
Findings
Mathematical formulation of differential calculus on graded jet manifolds
Cohomology structure of graded infinite order jet manifolds
Application to Lagrangian theories with even and odd variables
Abstract
The relevant material on differential calculus on graded infinite order jet manifolds and its cohomology is summarized. This mathematics provides the adequate formulation of Lagrangian theories of even and odd variables on smooth manifolds in terms of the Grassmann-graded variational bicomplex.
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