Lagrangian approach to local symmetries and self-dual model in gauge invariant formulation

Taking the St\"uckelberg Lagrangian associated with the abelian self-dual model of P.K. Townsend et al as a starting point, we embed this mixed first- and second-class system into a pure first-class system by following systematically the generalized Hamiltonian approach of Batalin, Fradkin and Tyutin. The resulting Lagrangian possesses an extended gauge invariance and provides a non-trivial example for a general Lagrangian approach to unravelling the full set of local symmetries of a Lagrangian.Comment: LaTeX, 15 page

Quantization of spontaneously broken gauge theory based on the BFT-BFV Formalism

We quantize the spontaneously broken abelian U(1) Higgs model by using the improved BFT and BFV formalisms. We have constructed the BFT physical fields, and obtain the first class observables including the Hamiltonian in terms of these fields. We have also explicitly shown that there are exact form invariances between the second class and first class quantities. Then, according to the BFV formalism, we have derived the corresponding Lagrangian having U(1) gauge symmetry. We also discuss at the classical level how one easily gets the first class Lagrangian from the symmetry-broken second class Lagrangian.Comment: 16 pages, latex, final version published in Mod. Phys. Lett.

Symmetries of SU(2) Skyrmion in Hamiltonian and Lagrangian approaches

We apply the Batalin-Fradkin-Tyutin (BFT) method to the SU(2) Skyrmion to study the full symmetry structure of the model at the first class Hamiltonian level. On the other hand, we also analyze the symmetry structure of the action having the WZ term, which corresponds to this Hamiltonian, in the framework of the Lagrangian approach. Furthermore, following the BFV formalism we derive the BRST invariant gauge fixed Lagrangian from the above extended action.Comment: 14 pages, final revised version, to appear in Mod. Phys. Lett.

Generalized BFT Formalism of Electroweak Theory in the Unitary Gauge

We systematically embed the SU(2)$\times$U(1) Higgs model in the unitary gauge into a fully gauge-invariant theory by following the generalized BFT formalism. We also suggest a novel path to get a first-class Lagrangian directly from the original second-class one using the BFT fields.Comment: 14 pages, Latex, no figure

BRST Quantization of the Proca Model based on the BFT and the BFV Formalism

The BRST quantization of the Abelian Proca model is performed using the Batalin-Fradkin-Tyutin and the Batalin-Fradkin-Vilkovisky formalism. First, the BFT Hamiltonian method is applied in order to systematically convert a second class constraint system of the model into an effectively first class one by introducing new fields. In finding the involutive Hamiltonian we adopt a new approach which is more simpler than the usual one. We also show that in our model the Dirac brackets of the phase space variables in the original second class constraint system are exactly the same as the Poisson brackets of the corresponding modified fields in the extended phase space due to the linear character of the constraints comparing the Dirac or Faddeev-Jackiw formalisms. Then, according to the BFV formalism we obtain that the desired resulting Lagrangian preserving BRST symmetry in the standard local gauge fixing procedure naturally includes the St\"uckelberg scalar related to the explicit gauge symmetry breaking effect due to the presence of the mass term. We also analyze the nonstandard nonlocal gauge fixing procedure.Comment: 29 pages, plain Latex, To be published in Int. J. Mod. Phys.

Symplectic embedding and Hamilton-Jacobi analysis of Proca model

Following the symplectic approach we show how to embed the Abelian Proca model into a first-class system by extending the configuration space to include an additional pair of scalar fields, and compare it with the improved Dirac scheme. We obtain in this way the desired Wess-Zumino and gauge fixing terms of BRST invariant Lagrangian. Furthermore, the integrability properties of the second-class system described by the Abelian Proca model are investigated using the Hamilton-Jacobi formalism, where we construct the closed Lie algebra by introducing operators associated with the generalized Poisson brackets.Comment: 24 page