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Covariant canonical formulations of classical field theories

by Francois Gieres

Submission summary

As Contributors: Francois Gieres
Arxiv Link: https://arxiv.org/abs/2109.07330v2 (pdf)
Date submitted: 2021-10-25 15:02
Submitted by: Gieres, Francois
Submitted to: SciPost Physics Lecture Notes
Academic field: Physics
Specialties:
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical

Abstract

We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories) and we discuss the relationships between these approaches as well as the relation with the standard (non-covariant) Hamiltonian formulation. Particular attention is paid to conservation laws related to Poincar\'e invariance within the different approaches. To make the text accessible to a wider audience, we have included an outline of Poisson and symplectic geometry for both classical mechanics and field theory.

Current status:
Editor-in-charge assigned


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Submission 2109.07330v2 on 25 October 2021

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