A description of classical field equations using extensions of graded Poisson brackets
Abstract
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 degree, in a similar way that ordinary Poisson brackets provide in mechanics. To illustrate the theory, we apply the results to the study of regular Lagrangians and Yang–Mills theories.
Fields of Study & Subjects
Numerical methods for differential equations
Algebraic and Geometric Analysis
Nonlinear Waves and Solitons
Publication details
- Journal / source
- International Journal of Geometric Methods in Modern Physics
- Publisher
- World Scientific Pub Co Pte Ltd
- Publication date
- 14 May 2026
- Language
- EN