In this paper the SU(2) Skyrme model will be reformulated as a gauge theory and the hidden symmetry will be investigated and explored in the energy spectrum computation. To this end we purpose a new constraint conversion scheme, based on the symplectic framework with the introduction of Wess-Zumino (WZ) terms in an unambiguous way. It is a positive feature not present on the BFFT constraint conversion. The Dirac's procedure for the first-class constraints is employed to quantize this gauge invariant nonlinear system and the energy spectrum is computed. The finding out shows the power of the symplectic gauge-invariant formalism when compared with another constraint conversion procedures present on the literature.

Inspired in some works about quantization of dissipative systems, in particular of the damped harmonic oscillator[1, 2, 3], we consider the dissipative system of a charge interacting with its own radiation, which originates the radiation damping (RD). Using the indirect Lagrangian representation we obtained a Lagrangian formalism with a Chern-Simons-like term. A Hamiltonian analysis is also done, what leads to the quantization of the system.

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In this paper, the analog of Maxwell electromagnetism for hydrodynamic turbulence, the metafluid dynamics, is extended in order to reformulate the metafluid dynamics as a gauge field theory. That analogy opens up the possibility to investigate this theory as a constrained system. Having this possibility in mind, we propose a Lagrangian to describe this new theory of turbulence and, subsequently, analyze it from the symplectic point of view. From this analysis, a hidden gauge symmetry is revealed, providing a clear interpretation and meaning of the physics behind the metafluid theory. Also, the geometrical interpretation to the gauge symmetries is discussed.

We show that a complete covariantization of the chiral constraint in the Floreanini-Jackiw necessitates an infinite number of auxiliary Wess-Zumino fields otherwise the covariantization is only partial and unable to remove the nonlocality in the chiral boson operator. We comment on recent works that claim to obtain covariantization through the use of Batalin-Fradkin-Tyutin method, that uses just one Wess-Zumino field.The quantization of chiral boson in two-dimensions is a very interesting theoretical problem, which has appeared originaly in the investigation of heterotic string [1], and became quite important in the study of fractional quantum Hall efect [2]. This problem has a simple solution in the Hamiltonian language while it has been beset with enormous difficulties in the Lagrangian side. One of these problems is the covariantization of the second-class chiral constraint, i.e., the transformation from second to first-class, which is the object of investigation in this paper.The usual Lagrangian route to chiral bosonization starts with a scalar field and projects out one of the chiral components by means of the chiral constraint ∂ ± φ ≈ 0. According to Dirac's theory of constrained systems [3], this is a second-class constraint, but in order to avoid the Lagrange multiplier to become dynamical, one needs it to be first-class. There has been two main routes to the covariantization of the chiral constraint. Siegel [4] proposed to set to zero one component of the energymomentum tensor resulting an action with the chiral constraint squared, which has a reparametrization invariance called as Siegel symmetry. In the quantum level, however, Siegel symmetry becomes second-class again on account of the central extension of the conformal algebra of the energy-momentum tensor [5]. A simple solution to the anomaly problem was given by Hull with the introduction of a new set of auxiliary fields called as no-movers [6]. Besides the anomaly problem, to produce first-class constraints by squaring second-class constraints has been criticized [7]. This sort of primary constraint does not produce the complete set of constraints when Dirac's algorithm is employed, and is (infinitely) reducible.The second route to covariantization starts with the Floreanini-Jackiw model[8] which is a singular theory from Dirac's point of view, the resulting constraint being the second-class chiral constraint. The constraint's nature is changedà la Faddeev-Shatashvili[9] with the introduction of Wess-Zumino auxiliary fields. The covariantization of the chiral constraint in this route has been proposed in two conceptually differents papers: in Ref. [10], an infinite family of scalar fields, coupled by a combination of right and left chiral constraints carefully adjusted to be first-class from the start, was shown to have a single chiral boson in the spectrum by use of very elegant group theoretical methods. In Ref.[11], the FJ chiral boson was iteratively changed to modify the nature of chiral constraint to render it first-class. Following this ro...

A formulation of Skyrme model as an embedded gauge theory with the constraint deformed away from the spherical geometry is proposed. The gauge invariant formulation is obtained firstly generalizing the intrinsic geometry of the model and then converting the constraint to first-class through an iterative Wess-Zumino procedure. The gauge invariant model is quantized via Dirac method for first-class system. A perturbative calculation provides new free parameters related to deformation that improve the energy spectrum obtained in earlier approaches.

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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.