Momentum section on Courant algebroid and constrained Hamiltonian mechanics
arXiv:2104.12091 · doi:10.1016/j.geomphys.2021.104350
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.
arXiv comment37 pages
References in corpus (17)
- Geometry of Batalin-Vilkovisky quantization
- Courant algebroids, derived brackets and even symplectic supermanifolds
- Derived brackets
- AKSZ-BV Formalism and Courant Algebroid-induced Topological Field Theories
- Chern-Simons Gauge Theory coupled with BF Theory
- Superfield BRST Charge and the Master Action
- Lie Algebroid Yang Mills with Matter Fields
- Lie algebroids, gauge theories, and compatible geometrical structures
- Gauging without Initial Symmetry
- Integration of Exact Courant Algebroids
- Q-algebroids and their cohomology
- BRST model applied to symplectic geometry
- Symplectic structures on the integration of exact Courant algebroids
- Momentum sections in Hamiltonian mechanics and sigma models
- The homotopy momentum map of general relativity
- Lie rackoids integrating Courant algebroids
- Groupoid symmetry, constraints and quantization of General Relativity