Alternative symplectic structures for SO(3,1) and SO(4) four-dimensional BF theories

Abstract

The most general action, quadratic in the B fields as well as in the curvature F, having SO(3,1) or SO(4) as the internal gauge group for a four-dimensional BF theory is presented and its symplectic geometry is displayed. It is shown that the space of solutions to the equations of motion for the BF theory can be endowed with symplectic structures alternative to the usual one. The analysis also includes topological terms and cosmological constant. The implications of this fact for gravity are briefly discussed.

13 pages, LaTeX file, no figures

References in corpus (3)

• Covariant canonical formalism for four-dimensional BF theory
• Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures
• Covariant description of parametrized nonrelativistic Hamiltonian systems

Cited by in corpus (4)

• Flipped spinfoam vertex and loop gravity
• A Immirzi-like parameter for 3d quantum gravity
• Two-dimensional topological field theories coupled to four-dimensional BF theory
• Topological field theories in n-dimensional spacetimes and Cartan's equations