Gauge symmetry of the chiral Schwinger model from an improved gauge unfixing formalism

Abstract

In this paper, the Hamiltonian structure of the bosonized chiral Schwinger model (BCSM) is analyzed. From the consistency condition of the constraints obtained from the Dirac method, we can observe that this model presents, for certain values of the α parameter, two second-class constraints, which means that this system does not possess gauge invariance. However, we know that it is possible to disclose gauge symmetries in such a system by converting the original second-class system into a first-class one. This procedure can be done through the gauge unfixing (GU) formalism by acting with a projection operator directly on the original second-class Hamiltonian, without adding any extra degrees of freedom in the phase space. One of the constraints becomes the gauge symmetry generator of the theory and the other one is disregarded. At the end, we have a first-class Hamiltonian satisfying a first-class algebra. Here, our goal is to apply a new scheme of embedding second-class constrained systems based on the GU formalism, named improved GU formalism, in the BCSM. The original second-class variables are directly converted into gauge invariant variables, called GU variables. We have verified that the Poisson brackets involving the GU variables are equal to the Dirac brackets between the original second-class variables. Finally, we have found that our improved GU variables coincide with those obtained from an improved BFT method after a particular choice for the Wess-Zumino terms.

A basic examination of the gauged model of the Floreanini-Jackiw chiral boson within the framework of BRST symmetry

“…However kinetic energy-like terms [29], and even the combination of mass-like and kinetic energy-like terms [33] are found to materialize as a counter term. A very recent study related to gauge symmetry (gauge unfixing) of chiral bosons is found in [34] and similar types of studies on non-commutative chiral boson is considered in [35]. Application of the gauge unfixing in the chiral Schwinger model is reported in [36].…”

Modified gauge-unfixing formalism and gauge symmetries in the noncommutative chiral bosons theory

“…Concerning gauge achievability, the gauge-fixing function Γ 1 must be chosen in such a way that the determinant in the integration measure in (54) does not vanish. This concludes the functional quantization of the gauge-invariant description of the NCCB, with gauge transformations generated by Ω 1 .…”

“…Nonetheless, we claim that a consistent NCCB abelianization can be done without the need of any auxiliary fields whatsoever. That is one of the main advantages of the gauge-unfixing (GU) method [47][48][49][50][51][52][53][54][55]. Building on the original work of Mitra and Rajaraman [47], which first conjectured the interpretation of second-class constraints in phase space as resulting from gauge-fixing conditions within a larger gauge-invariant theory, Anishetty and Vytheeswaran constructed a Lie projection operator, whose action in the second-class functions was able to reveal hidden symmetries [48][49][50].…”

“…Building on the original work of Mitra and Rajaraman [47], which first conjectured the interpretation of second-class constraints in phase space as resulting from gauge-fixing conditions within a larger gauge-invariant theory, Anishetty and Vytheeswaran constructed a Lie projection operator, whose action in the second-class functions was able to reveal hidden symmetries [48][49][50]. Those ideas were further elaborated to produce the improved or modified gauge-unfixing formalism [51,52], centered on the construction of the invariant GU variables, and have found recent appeal in quantum field theory [53][54][55]. In this way, the main goal of the present letter is to develop a gauge-invariant theory for the NCCB model, without auxiliary fields, by directly applying the modified GU formalism [51][52][53][54][55] to the noncommutative fields space.…”

“…Those ideas were further elaborated to produce the improved or modified gauge-unfixing formalism [51,52], centered on the construction of the invariant GU variables, and have found recent appeal in quantum field theory [53][54][55]. In this way, the main goal of the present letter is to develop a gauge-invariant theory for the NCCB model, without auxiliary fields, by directly applying the modified GU formalism [51][52][53][54][55] to the noncommutative fields space.…”