Hamiltonian study for Chern-Simons and Pontryagin theories

Abstract

The Hamiltonian analysis for the Chern-Simons theory and Pontryagin invariant, which depends of a connection valued in the Lie algebra of SO(3,1), is performed. By applying a pure Dirac's method we find for both theories the extended Hamiltonian, the extended action, the constraint algebra, the gauge transformations and we carry out the counting of degrees of freedom. From the results obtained in the present analysis, we will conclude that the theories under study have a closed relation among its constraints and defines a topological field theory. In addition, we extends the configuration space for the Pontryagin theory and we develop the Hamiltonian analysis for this modified version, finding a best description of the results previously obtained.

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Cited by in corpus (13)

• A pure Dirac's canonical analysis for four-dimensional BF theories
• Hamiltonian dynamics and gauge symmetry for three-dimensional Palatini theory with cosmological constant
• Hamiltonian dynamics of an exotic action for gravity in three dimensions
• Faddeev-Jackiw quantization of four dimensional BF theory
• Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes
• On the Faddeev-Jackiw Symplectic Framework for Topologically Massive Gravity
• Hamiltonian analysis of a topological theory in the presence of boundaries
• Dirac's and Generalized Faddeev-Jackiw brackets for Einstein's theory in G $\to 0$ limit
• Canonical and symplectic analysis for three dimensional gravity without dynamics
• A pure Dirac's method for Husain-Kuchar theory
• Constructing the theory at the boundary, its dynamics and degrees of freedom
• Discrete canonical analysis of three dimensional gravity with cosmological constant
• The Hamilton-Jacobi characteristic equations for topological invariants: Pontryagin and Euler classes