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

Journal Article · Sun Apr 15 04:00:00 EDT 2018 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2018.02.003· OSTI ID:22848312

Escalante, Alberto

Highlights: •We report the symplectic analysis for Euler and Pontryagin invariants. •We report the Faddeev–Jackiw constraints. •A symplectic tensor is constructed. •The generalized Faddeev–Jackiw brackets are found. •The quantum Faddeev–Jackiw constraints are solved. -- 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.

• OSTI ID: 22848312
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 391; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
EQUATIONS OF MOTION
FOUR-DIMENSIONAL CALCULATIONS
LIMITING VALUES
QUANTIZATION
QUANTUM STATES
TENSORS