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

2025/07/07 by Manuel de León, Rubén Izquierdo-López, de León, Manuel +1
#35B06 #53D42 #53Z05 #70S20 #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2507.04743

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.

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