Duality through the symplectic embedding formalism

Abstract

In this work we show that we can obtain dual equivalent actions following the symplectic formalism with the introduction of extra variables which enlarge the phase space. We show that the results are equal as the one obtained with the recently developed gauging iterative Noether dualization method (NDM). We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method (SEM) is more profound since it can reveal a whole family of dual equivalent actions. We illustrate the method demonstrating that the gauge-invariance of the electromagnetic Maxwell Lagrangian broken by the introduction of an explicit mass term and a topological term can be restored to obtain the dual equivalent and gauge-invariant version of the theory.

RevTeX4, 10 pages. To appear in Int. J. Mod. Phys. A

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• Faddeev-Jackiw quantization of four dimensional BF theory
• Faddeev-Jackiw quantization of topological invariants: Euler and Pontryagin classes
• Dirac's and Generalized Faddeev-Jackiw brackets for Einstein's theory in G $\to 0$ limit
• QCD gauge symmetries through Faddeev-Jackiw symplectic method
• Canonical and symplectic analysis for three dimensional gravity without dynamics
• Hamilton-Jacobi analysis for three dimensional gravity without dynamics
• Electromagnetic Dualities on Noncommutative Space-Time and Symplectic Formalisms