Momentum section on Courant algebroid and constrained Hamiltonian mechanics

TL;DR

This paper generalizes the concept of momentum maps to Courant algebroids, linking symplectic geometry, Lie algebroids, and Hamiltonian mechanics, and develops cohomological formulations using BFV and BV formalisms.

Contribution

It introduces a new framework for momentum sections within Courant algebroids and applies it to constrained Hamiltonian systems, extending existing theories.

Findings

Identified momentum sections in Courant algebroid symmetric systems.

Constructed cohomological formulations using BFV and BV formalisms.

Developed the Weil algebra for the new structure.

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.