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Covariant canonical formulations of classical field theories

by Francois Gieres

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Submission summary

Authors (as registered SciPost users): Francois Gieres
Submission information
Preprint Link:  (pdf)
Date accepted: 2023-11-06
Date submitted: 2023-10-26 12:12
Submitted by: Gieres, Francois
Submitted to: SciPost Physics Lecture Notes
Ontological classification
Academic field: Physics
  • Gravitation, Cosmology and Astroparticle Physics
  • High-Energy Physics - Theory
  • Mathematical Physics
Approach: Theoretical


We review in simple terms the covariant approaches to the canonical formulation of classical relativistic field theories (in particular gauge field theories and general relativity) 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 (notably related to geometric symmetries) within the different approaches. Moreover, for each of these approaches, the impact of space-time boundaries is also addressed. 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.

List of changes

Text cut modified above eq. (4.15)
(as requested by one of the referee's)

Published as SciPost Phys. Lect. Notes 77 (2023)

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