Chiral Schwinger model based on the Batalin-Fradkin-Vilkovisky formalism

Abstract

We quantize the bosonized chiral Schwinger model by using the systematic Batalin-FradkinVilkovisky formalism. We derive a Becchi-Rouet-Stora-Tyutin gauge-fixed covariant action showing that the auxiliary fields introduced in the formalism turn into the Wess-Zumino scalar.

Batalin-Tyutin quantization of the chiral Schwinger model

“…We have applied the FIK method to the bosonized chiral Schwinger model (CSM) [4]. Recently, Banerjee, Rothe, and Rothe [5] have pointed out that the FIK analyses [3,4] are not a systematic application of the BFV formalism. After their work, Banerjee [6] has systematically applied Batalin-Tyutin (BT) Hamiltonian method [7] to the second class constraint system of the abelian Chern-Simons (CS) field theory [8][9][10].…”

Symplectic Embedding and Hamilton–jacobi Analysis of Proca Model

“…On the other hand, the Becci-Rouet-StoraTyutin (BRST) [2,3] quantization of constrained systems along the lines originally established by Batalin, Fradkin, and Vilkovisky [4,5], and then reformulated in a more tractable and elegant version by Batalin, Fradkin, and Tytin [6], does not suffer from these difficulties, as it relies on a simple Poisson bracket structure. As a result, the embedding of secondclass systems into first-class ones (gauge theories) has received much attention in the past years and the DQM improved in this way, has been applied to a number of models [7][8][9][10][11][12][13] in order to obtain the corresponding Wess-Zumino (WZ) actions [14,15]. In fact, the earlier work on this subject is based on the traditional Dirac's pioneering work [1], which has been criticized for introducing "superfluous" primary constraints, and has been avoided in more recent treatments, based on the symplectic structure of phase space.…”

Remarks on Generalized Uncertainty Principle Induced From Constraint System

“…It means that the Hamiltonian system described by the GUP brackets can be interpreted as a gauge fixed version of the first class constraint system. The similar behaviors can be found in the chiral Schwinger model [19][20][21] and the Chern-Simons theory [22][23][24].…”