Momentum section on Courant algebroid and constrained Hamiltonian mechanics

Abstract

We propose a generalization of the momentum map on a symplectic manifold with a Lie algebra action to a Courant algebroid structure. The theory of a momentum section on a Lie algebroid is generalized to the theory compatible with a Courant algebroid. As an example, we identify the momentum section in a constrained Hamiltonian mechanics with Courant algebroid symmetry. Moreover, we construct cohomological formulations by considering the BFV and BV formalism of this Hamiltonian system. The Weil algebra for this structure is constructed.

37 pages

References in corpus (3)

• AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
• Lie Algebroid Yang Mills with Matter Fields
• The homotopy momentum map of general relativity

Cited by in corpus (4)

• Homotopy momentum sections on multisymplectic manifolds
• Comomentum sections and Poisson maps in Hamiltonian Lie algebroids
• Higher dimensional Lie algebroid sigma model with WZ term
• Compatible $E$-Differential Forms on Lie Algebroids over (Pre-)Multisymplectic Manifolds