Symplectic formulation of teleparallel gravity
- Resource Type
- Authors
- Arief Hermanto; Luh Putu Budi Yasmini; Muhammad Farchani Rosyid
- Source
- International Journal of Geometric Methods in Modern Physics. 17:2050096
- Subject
- Gravity (chemistry)
Physics and Astronomy (miscellaneous)
Structure (category theory)
law.invention
General Relativity and Quantum Cosmology
symbols.namesake
law
symbols
Noether's theorem
Mathematics::Symplectic Geometry
Manifold (fluid mechanics)
Symplectic geometry
Mathematics
Mathematical physics
- Language
- ISSN
- 1793-6977
0219-8878
Teleparallel gravity has been formulated in the symplectic-geometrical fashion. For that purpose, the symplectic potential and the pre-symplectic structure on the manifold of all solutions of the field equation of teleparallel gravity have been firstly constructed from the Lagrangian density of the theory. That the obtained pre-symplectic structure is a symplectic structure also has been proved. It has been shown that the symplectic potential obtained from the Lagrangian density up to a factor is equal to the superpotential of teleparallel gravity. The Hamiltonian formulation of teleparallel gravity has been derived. Furthermore, the Poisson bracket between arbitrary two classical observables (i.e. real-valued functional) defined on the symplectic manifold of all solutions of the field equation of teleparallel gravity has constructed. The Hamiltonian vector field associated to an observable has been obtained. The formulation of Noether theorem in the symplectic formulation of teleparallel gravity has been investigated.