Covariant Variational Evolution and Jacobi Brackets: Fields
Florio M. Ciaglia, Fabio Di Cosmo, Alberto Ibort, Giuseppe Marmo and, Luca Schiavone
TL;DR
This paper extends the covariant brackets framework within contact geometry to the multisymplectic formulation of free field theories like Klein-Gordon and Schrödinger, providing new insights into their geometric structure.
Contribution
It introduces an extension of covariant brackets analysis to multisymplectic formulations of key free field theories, enriching the geometric understanding of their solution spaces.
Findings
Extended covariant brackets to Klein-Gordon and Schrödinger theories
Demonstrated geometric structures in multisymplectic formulations
Enhanced understanding of solution space geometry in field theories
Abstract
The analysis of the covariant brackets on the space of functions on the solutions to a variational problem in the framework of contact geometry initiated in the companion letter Ref.19 is extended to the case of the multisymplectic formulation of the free Klein-Gordon theory and of the free Schr\"{o}dinger equation.
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