Covariant Brackets for Particles and Fields

Abstract

A geometrical approach to the covariant formulation of the dynamics of relativistic systems is introduced. A realization of Peierls brackets by means of a bivector field over the space of solutions of the Euler-Lagrange equations of a variational principle is presented. The method is illustrated with some relevant examples.

14 pages

References in corpus (3)

• Geometry of quantum systems: density states and entanglement
• Covariant Poisson Brackets in Geometric Field Theory
• Covariant phase space, constraints, gauge and the Peierls formula

Cited by in corpus (6)

• Multisymplectic Constraint Analysis of Scalar Field Theories, Chern-Simons Gravity, and Bosonic String Theory
• Symmetries and Covariant Poisson brackets on pre-symplectic manifolds
• Covariant Variational Evolution and Jacobi Brackets: Fields
• Covariant Variational Evolution and Jacobi Brackets: Particles
• The Geometry of the solution space of first order Hamiltonian field theories I: from particle dynamics to free Electrodynamics
• Covariant reduction of classical Hamiltonian Field Theories: From D'Alembert to Klein-Gordon and Schrödinger