C. Neves

Gauging the SU(2) Skyrme model

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 propose a constraint conversion scheme, based on the symplectic framework with the introduction of Wess-Zumino terms in an unambiguous way. It is a positive feature not present in the Batalin-Fradkin-Fradkina-Tyutin constraint conversion. Diracs procedure for the first-class constraints is employed to quantize this gauge-invariant nonlinear system and the energy spectrum is computed. The result shows the power of the symplectic gauge-invariant formalism when compared with other constraint conversion procedures present in the literature.

On the covariantization of the chiral constraints

We show that a complete covariantization of the chiral constraint in the Floreanini-Jackiw necessitates an infinite number of auxiliary Wess-Zumino fields other-wise 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.

DUALITY THROUGH THE SYMPLECTIC EMBEDDING FORMALISM

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. We believe that, with the arbitrariness property of the zero mode, the symplectic embedding method 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.

THE DUAL EMBEDDING METHOD IN D = 3

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.

Open string with a background B field as the first order mechanics, noncommutativity, and soldering formalism

To study noncommutativity properties of the open string with constant B field, we construct a mechanical action that reproduces classical dynamics of the string sector under consideration. It allows one to apply the Dirac quantization procedure for constrained systems in a direct and unambiguous way. The mechanical action turns out to be the first order system without taking the strong field limit B{yields}{infinity}. In particular, it is true for the zero mode of the string coordinate, which means that the noncommutativity is an intrinsic property of this mechanical system. We describe the arbitrariness in the relation existing between the mechanical and the string variables and show that noncommutativity of the string variables on the boundary can be removed. This is in correspondence with the result of Seiberg and Witten on the relation among noncommutative and ordinary Yang-Mills theories. The recently developed soldering formalism helps us to establish a connection between the original open string action and the Polyakov action.

Symplectic embedding of second class systems

Abstract An alternative approach to embed second class systems using the Wess-Zumino (WZ) variables is proposed[1]. This is developed within the symplectic framework[2,3].

LAGRANGIAN FORMULATION FOR NONCOMMUTATIVE NONLINEAR SYSTEMS

In this work we study Lagrangian formulations for the noncommutative versions of the SU(2) Skyrme model and O(3) nonlinear sigma model. These formulations will be obtained using the Faddeev–Jackiw symplectic formalism. Other noncommutative Lagrangian formulations can be proposed and different noncommutative versions for these nonlinear systems can be obtained.

New considerations about the Maxwell-Podolsky-like theory through the symplectic embedding formalism

The Podolsky theory can be modified by changing the sign of the Maxwell term. In this case we have a Podolsky-like action with a different spectrum. This new theory was already analyzed by the literature at the propagator level. However, we believe that the results are inconclusive since a precise and entire comprehension, at the Lagrangian level, of this theory is still lacking. In this paper we show in an exact way, using the symplectic embedding formalism, that this Podolsky-like action is in fact dual equivalent to the Proca theory showing the same physical features.

An alternative approach to canonical quantizationof the radiation damping

Abstract.Inspired by some works on quantization of dissipative systems, in particular the ones treating the damped harmonic oscillator and by a paper due to Lukierski, we consider the dissipative system of a charge interacting with its own radiation, which is the origin of radiation damping. Using the indirect Lagrangian representation we obtained a Lagrangian formalism with a Chern-Simons-like term. A Hamiltonian analysis is also done in commutative and non-commutative scenarios, which leads to the quantization of the system.

Hamiltonian symplectic embedding of the massive noncommutative U(1) theory

We show that the massive noncommutative U(1) theory is embedded in a gauge theory using an alternative systematic way [1], which is based on the symplectic framework. The embedded Hamiltonian density is obtained after a finite number of steps in the iterative symplectic process as opposed to the result proposed using the BFFT formalism [2]. This alternative formalism of embedding shows how to get a set of dynamically equivalent embedded Hamiltonian densities.