Convenient partial Poisson manifolds

Pelletier, Fernand; Cabau, Patrick

doi:10.1016/j.geomphys.2018.10.017

Cited by 9 publications

(8 citation statements)

References 7 publications

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“…According to (2), if we set a = p A •X and X = ρ(X), the pair (a, X) is well defined and from the definition of T A M the relation ( 19) is satisfied. Conversely, if a is a section a of A and X a vector field on V, the relation (19) means exactly that X(m) = ( p(a(m)), X(m)) belongs to T A m M; so we get a section X of T A M. Now it is clear that a = p A • X and X = ρ(X).…”

Section: Lie Morphisms and Lie Algebroid Morphisms Letmentioning

confidence: 99%

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Prolongations of convenient Lie algebroids

Cabau¹,

Pelletier²

2020

Preprint

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Section: Lie Morphisms and Lie Algebroid Morphisms Letmentioning

confidence: 99%

“…Conversely such a pair (a, X) which satisfies (19) defines a unique section X on V, the associated pair of X is precisely (a, X) and with these notations, we have ρ(X) = X.…”

Section: Lie Morphisms and Lie Algebroid Morphisms Letmentioning

confidence: 99%

Prolongations of convenient Lie algebroids

Cabau¹,

Pelletier²

2020

Preprint

Self Cite

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“…The expression of ℓ is not uniquely defined by condition (367) since this relation is invariant under the following transformations: corner ambiguity :…”

Section: Construction Of Noether Charges Following Wald and Zoupasmentioning

confidence: 99%

Covariant canonical formulations of classical field theories

Gieres

2023

SciPost Phys. Lect. Notes

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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.

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“…Andrée Bastiani in her Ph.D. thesis [268] and which is considered in works of field theory [230]), we refer to [246,263,269] and the appendix of [270]. By way of conclusion, we may say that, in dealing with geometric structures on a space of classical fields in theoretical physics, a minimum of mathematical rigor is required to take into account physically important aspects like degeneracies.…”

Section: C10 On Infinite-dimensional Vector Spaces and Manifoldsmentioning

confidence: 99%

Covariant canonical formulations of classical field theories

Gieres¹

2021

Preprint

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who established many original and profound results in pure mathematics which found important applications in physics to which he also contributed substantially by his work and his action. By his wonderful lectures he conveyed his broad knowledge while highlighting the essential points and casting the physical concepts in their appropriate mathematical setting. An outstanding, undogmatic and open-minded mathematician of great simplicity and generosity left us while leaving a lasting impression on all those who had the chance to meet him.

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Convenient partial Poisson manifolds

Cited by 9 publications

References 7 publications

Prolongations of convenient Lie algebroids

Prolongations of convenient Lie algebroids

Covariant canonical formulations of classical field theories

Covariant canonical formulations of classical field theories

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