A pure Dirac's canonical analysis for four-dimensional BF theories

Abstract

We perform Dirac's canonical analysis for a four-dimensional $BF$ and for a generalized four-dimensional $BF$ theory depending on a connection valued in the Lie algebra of SO(3,1). This analysis is developed by considering the corresponding complete set of variables that define these theories as dynamical, and we find out the relevant symmetries, the constraints, the extended Hamiltonian, the extended action, gauge transformations and the counting of physical degrees of freedom. The results obtained are compared with other approaches found in the literature.

Submitted to Journal of Physics A, Mathematical and Theoretical

References in corpus (6)

• Hamiltonian Analysis of non-chiral Plebanski Theory and its Generalizations
• Covariant canonical formalism for four-dimensional BF theory
• Hamiltonian study for Chern-Simons and Pontryagin theories
• Hamiltonian dynamics of extended objects: Regge-Teitelboim model
• Hamiltonian dynamics for Einstein's action in G$\to$0 limit
• Two-dimensional topological field theories coupled to four-dimensional BF theory

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• Poincare-Plebanski formulation of GR and dual simplicity constraints
• Dirac's and Generalized Faddeev-Jackiw brackets for Einstein's theory in G $\to 0$ limit
• Hamiltonian Analysis of Pre-geometric Gravity
• New canonical analysis for higher order topologically massive gravity
• Perturbative BF theory
• Canonical and symplectic analysis for three dimensional gravity without dynamics
• Covariant momentum map for non-Abelian topological BF field theory
• Hamiltonian analysis for abelian and non-abelian massive theories in three dimensions