28 research outputs found
A proposal for a first class conversion formalism based on the symmetries of the Wess-Zumino terms
We propose a new procedure to embed second class systems by introducing
Wess-Zumino (WZ) fields in order to unveil hidden symmetries existent in the
models. This formalism is based on the direct imposition that the new
Hamiltonian must be invariant by gauge-symmetry transformations. An
interesting feature in this approach is the possibility to find a
representation for the WZ fields in a convenient way, which leads to preserve
the gauge symmetry in the original phase space. Consequently, the
gauge-invariant Hamiltonian can be written only in terms of the original
phase-space variables. In this situation, the WZ variables are only auxiliary
tools that permit to reveal the hidden symmetries present in the original
second class model. We apply this formalism to important physical models: the
reduced-SU(2) Skyrme model, the Chern-Simons-Proca quantum mechanics and the
chiral bosons field theory. In all these systems, the gauge-invariant
Hamiltonians are derived in a very simple way.Comment: Revised version. Title changed for Gauging by symmetries. To appear
in IJMP
The SU(2) Skyrme model and anomaly
The SU(2) Skyrme model,expanding in the collective coordinates variables,
gives rise to second-class constraints. Recently this system was embedded in a
more general Abelian gauge theory using the BFFT Hamiltonian method. In this
work we quantize this gauge theory computing the Noether current anomaly using
for this two different methods: an operatorial Dirac first class formalism and
the non-local BV quantization coupled with the Fujikawa regularization
procedure.Comment: 6 pages, Revtex. Final version to be published in Physics Letters
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 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.Comment: revised version, to appear in Phys.Rev.
Operatorial quantization of Born-Infeld Skyrmion model and hidden symmetries
The SU(2) collective coordinates expansion of the Born-Infeld\break Skyrmion
Lagrangian is performed. The classical Hamiltonian is computed from this
special Lagrangian in approximative way: it is derived from the expansion of
this non-polynomial Lagrangian up to second-order variable in the collective
coordinates. This second-class constrained model is quantized by Dirac
Hamiltonian method and symplectic formalism. Although it is not expected to
find symmetries on second-class systems, a hidden symmetry is disclosed by
formulating the Born-Infeld Skyrmion %model as a gauge theory. To this end we
developed a new constraint conversion technique based on the symplectic
formalism. Finally, a discussion on the role played by the hidden symmetry on
the computation of the energy spectrum is presented.Comment: A new version of hep-th/9901133. To appear in JP
Lagrangian formulation for noncommutative nonlinear systems
In this work we use the well known formalism developed by Faddeev and Jackiw
to introduce noncommutativity within two nonlinear systems, the SU(2) Skyrme
and O(3) nonlinear sigma models. The final result is the Lagrangian
formulations for the noncommutative versions of both models. The possibility of
obtaining different noncommutative versions for these nonlinear systems is
demonstrated.Comment: 8 pages. Revex 4.