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 (10)

• Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action
• so(4) Plebanski Action and Relativistic Spin Foam Model
• Classical Euclidean general relativity from ``left-handed area = right-handed area"
• BF gravity and the Immirzi parameter
• Covariant canonical formalism for four-dimensional BF theory
• Towards a Gravitational Analog to S-duality in Non-abelian Gauge Theories
• Self-dual gravity with topological terms
• Symplectic quantization, inequivalent quantum theories, and Heisenberg's principle of uncertainty
• Covariant description of parametrized nonrelativistic Hamiltonian systems
• Hamilton-Jacobi theory for Hamiltonian systems with non-canonical symplectic structures

Cited by in corpus (14)

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• Phase space descriptions for simplicial 4d geometries
• $BF$ gravity
• On the Relations between Gravity and BF Theories
• A Immirzi-like parameter for 3d quantum gravity
• Hamiltonian study for Chern-Simons and Pontryagin theories
• Lorentz-covariant Hamiltonian analysis of BF gravity with the Immirzi parameter
• Two-dimensional topological field theories coupled to four-dimensional BF theory
• Topological field theories in n-dimensional spacetimes and Cartan's equations
• BF gravity with Immirzi parameter and cosmological constant
• BF gravity with Immirzi parameter and matter fields
• Barbero's formulation from a $BF$-type action with the Immirzi parameter
• Equivalent and Alternative Forms for BF Gravity with Immirzi Parameter
• Comment on "Dimension of the Moduli Space and Hamiltonian Analysis of BF Field Theories"