On Covariant Poisson Brackets in Field Theory

DOI10.1007/978-3-319-18212-4_12zbMATH Open1366.70033arXiv1412.2902OpenAlexW1581097311MaRDI QIDQ3460599

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Publication date: 8 January 2016

Published in: Trends in Mathematics (Search for Journal in Brave)

Abstract: A general approach is proposed to constructing covariant Poisson brackets in the space of histories of a classical field-theoretical model. The approach is based on the concept of Lagrange anchor, which was originally developed as a tool for path-integral quantization of Lagrangian and non-Lagrangian dynamics. The proposed covariant Poisson brackets generalize the Peierls' bracket construction known in the Lagrangian field theory.

Full work available at URL: https://arxiv.org/abs/1412.2902

zbMATH Keywords

Lagrange anchorcovariant phase spacePeierls' bracket

Mathematics Subject Classification ID

Lagrangian formalism and Hamiltonian formalism in mechanics of particles and systems (70S05) Alternative quantum mechanics (including hidden variables, etc.) (81Q65)

Related Items (7)

Three-dimensional relativistic-covariant Poisson brackets ⋮ Covariant formulation of field theories associated withp-branes ⋮ THE POISSON BRACKET FOR POISSON FORMS IN MULTISYMPLECTIC FIELD THEORY ⋮ Peierls brackets in non-Lagrangian field theory ⋮ Toward construction of a consistent field theory with Poincaré covariance in terms of step-function-type basis functions for gauge fields ⋮ Quantal Poincaré-Cartan integral invariant for field theory ⋮ Covariant Variational Evolution and Jacobi brackets: Fields

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