English

A description of classical field equations using extensions of graded Poisson brackets

Mathematical Physics 2025-07-08 v1 math.MP

Abstract

As it is well-known, Poisson brackets play a fundamental role both in mechanics and in classical field theories. In this paper we develop a theory of extensions of graded Poisson brackets in graded Dirac manifolds. We then show how these extensions can be used to obtain the field equations of a particular theory as well as the evolution of forms of arbitrary order, in a similar way that ordinary Poisson brackets provide in mechanics.

Keywords

Cite

@article{arxiv.2507.04743,
  title  = {A description of classical field equations using extensions of graded Poisson brackets},
  author = {Manuel de León and Rubén Izquierdo-López},
  journal= {arXiv preprint arXiv:2507.04743},
  year   = {2025}
}