Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes

Abstract

The symplectic analysis for the four dimensional Pontryagin and Euler invariants is performed within the Faddeev-Jackiw context. The Faddeev-Jackiw constraints and the generalized Faddeev-Jackiw brackets are reported; we show that in spite of the Pontryagin and Euler classes give rise the same equations of motion, its respective symplectic structures are different to each other. In addition, a quantum state that solves the Faddeev-Jackiw constraints is found, and we show that the quantum states for these invariants are different to each other. Finally, we present some remarks and conclusions.

References in corpus (5)

• Higher dimensional massive bigravity
• Hamiltonian study for Chern-Simons and Pontryagin theories
• Duality through the symplectic embedding formalism
• The dual embedding method in D=3
• Barbero's formulation from a $BF$-type action with the Immirzi parameter

Cited by in corpus (4)

• Faddeev-Jackiw Quantization of Christ-Lee Model
• Hamiltonian analysis of General Relativity and extended gravity from the iterative Faddeev-Jackiw symplectic approach
• The Hamilton-Jacobi characteristic equations for topological invariants: Pontryagin and Euler classes
• Hamilton-Jacobi analysis for three dimensional gravity without dynamics