The Dual Embedding Method in D = 3

Abstract

Improving the beginning steps of a previous work, we settle the dual embedding method (DEM) as an alternative and efficient method for obtaining dual equivalent actions also in D = 3. We show that we can obtain dual equivalent actions which were previously obtained in the literature using the gauging iterative Noether dualization method (NDM). We believe that, with the arbitrariness property of the zero mode, the DEM is more profound since it can reveal a whole family of dual equivalent actions. The result confirms the one obtained previously which is important since it has the same structure that appears in the Abelian Higgs model with an anomalous magnetic interaction.

Hořava–Lifshitz cosmological models with noncommutative phase space variables

“…Just few years after its publication, the FJ formalism was modified by Barcelos-Neto and Wotzasek in [38], by Montani and Wotzasek in [39], and through the years it has been used in different systems [40,41].…”

Symplectic Approach of Three-Dimensional Palatini Theory Plus a Chern-Simons Term

“…Furthermore, the matrix (22) is still singular; however, we have shown that there are no more constraints and that the theory has a gauge symmetry. In order to construct a symplectic tensor, we need to fix the gauge [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], and thus we will fix the temporal gauge, say, 0 = 0 = 0, which means thaṫ= 0 anḋ= 0. In this manner, the fixing gauge will be added to the symplectic Lagrangian via Lagrange multipliers, Θ and Ξ .…”

“…In this manner, with the antecedents mentioned above, in this paper, we will study the P-CS theory from a symplectic point of view. For this aim, we will use the symplectic formalism of Faddeev-Jackiw [FJ] [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], due basically to the fact that the FJ approach is more economical than Dirac's method. In fact, the FJ is a symplectic description where all relevant information of the theory can be obtained through a symplectic tensor, which is constructed from the symplectic variables that are identified from the Lagrangian.…”

Obtaining non-Abelian field theories via the Faddeev–Jackiw symplectic formalism

“…In recent works [6], the FJ symplectic formalism has been used in a systematic way for different purposes: the study of hidden symmetries, the construction of equivalent gauge theories (duality), noncommutative field theory, to solve the obstruction problem to the construction of the canonical Lagrangian formulation for rotational systems and other.…”