TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysLectNotes.77
TI  - Covariant canonical formulations of classical field theories
PY  - 2023/12/05
UR  - https://scipost.org/SciPostPhysLectNotes.77
JF  - SciPost Physics Lecture Notes
JA  - SciPost Phys. Lect. Notes
SP  - 77
A1  - Gieres, Francois
AB  - 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.
ER  -

@Article{10.21468/SciPostPhysLectNotes.77,
	title={{Covariant canonical formulations of classical field theories}},
	author={Francois Gieres},
	journal={SciPost Phys. Lect. Notes},
	pages={77},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysLectNotes.77},
	url={https://scipost.org/10.21468/SciPostPhysLectNotes.77},
}