Faddeevian Regularization Research Articles

Instant-Form and Light-Front Quantization of Field Theories

In this work we consider the instant-form and light-front quantization of some field theories. As an example, we consider a class of gauged non-linear sigma models with different regularizations. In particular, we present the path integral quantization of the gauged non-linear sigma model in the Faddeevian regularization. We also make a comparision of the possible differences in the instant-form and light-front quantization at appropriate places.

Light-Front Quantization of the Vector Schwinger Model with a Photon Mass Term in Faddeevian Regularization

In this talk, we study the light-front quantization of the vector Schwinger model with photon mass term in Faddeevian Regularization, describing two-dimensional electrodynamics with mass-less fermions but with a mass term for the U(1) gauge field. This theory is gauge-non-invariant (GNI). We construct a gauge-invariant (GI) theory using Stueckelberg mechanism and then recover the physical content of the original GNI theory from the newly constructed GI theory under some special gauge-fixing conditions (GFC’s). We then study LFQ of this new GI theory.

Vector Schwinger Model with a Photon Mass Term with Faddeevian Regularization

In this talk, we consider the vector Schwinger model with a photon mass term with Faddeevian Regularization, describing two-dimensional (2D) electrodynamics with mass-less fermions and study its Hamiltonian and path integral quantization. This theory is seen to be gauge-non-invariant (GNI). We then construct a gauge-invariant (GI) theory corresponding to this GNI theory using the Stueckelberg mechanism and then recover the physical content of the original GNI theory from the newly constructed GI theory under some special gauge-fixing conditions.

Hamiltonian, Path Integral and BRST Formulations of the Vector Schwinger Model with a Photon Mass Term with Faddeevian Regularization

Recently (in a series of papers) we have studied the vector Schwinger model with a photon mass term describing one-space one-time dimensional electrodynamics with mass-less fermions in the so-called standard regularization. In the present work, we study this model in the Faddeevian regularization (FR). This theory in the FR is seen to be gauge-non-invariant (GNI). We study the Hamiltonian and path integral quantization of this GNI theory. We then construct a gauge-invariant (GI) theory corresponding to this GNI theory using the Stueckelberg mechanism and recover the physical content of the original GNI theory from the newly constructed GI theory under some special gauge-choice. Further, we study the Hamiltonian, path integral and Becchi-Rouet-Stora and Tyutin formulations of the newly constructed GI theory under appropriate gauge-fixing conditions.

Chiral Thirring–Wess model with Faddeevian regularization

Replacing vector type of interaction of the Thirring–Wess model by the chiral type a new model is presented which is termed here as chiral Thirring–Wess model. Ambiguity parameters of regularization are so chosen that the model falls into the Faddeevian class. The resulting Faddeevian class of model in general does not possess Lorentz invariance. However we can exploit the arbitrariness admissible in the ambiguity parameters to relate the quantum mechanically generated ambiguity parameters with the classical parameter involved in the masslike term of the gauge field which helps to maintain physical Lorentz invariance instead of the absence of manifestly Lorentz covariance of the model. The phase space structure and the theoretical spectrum of this class of model have been determined through Dirac’s method of quantization of constraint system.

NON-ABELIAN GAUGED CHIRAL BOSON WITH A GENERALIZED FADDEEVIAN REGULARIZATION

We consider non-Abelian gauged version of chiral boson with a generalized Faddeevian regularization. It is a second-class constrained theory. We quantize the theory and analyze the phase space. It is shown that in spite of the lack of manifest Lorentz invariance in the action, it has a consistent and Poincaré invariant phase space structure.

CHIRAL QED IN TERMS OF CHIRAL BOSON WITH A GENERALIZED FADDEEVIAN REGULARIZATION

Chiral QED with a generalized Faddeevian regularization is considered. Imposing a chiral constraint a gauged version of Floreanini–Jackiw Lagrangian is constructed. The imposition of the chiral constraint has spoiled the manifestly Lorentz covariance structure of the theory. The phase space structure for this theory has been determined in the present situation. It is found that spectrum changes drastically but it remains Lorentz invariant in its constrained (physical) subspace. Chiral fermion disappears from the spectra and the photon acquire mass as well. Poincaré algebra has been calculated to show physical Lorentz invariance explicitly.

Hamiltonian and BRST formulations of a gauge-invariant chiral Schwinger model with the Faddeevian regularization

The Hamiltonian and BRST formulations of a gauge-invariant chiral Schwinger model with the Faddeevian regularization due to Mukhopadhyay and Mitra in one-space one-time dimensions (obtained by the inclusion of an appropriate Wess–Zumino term in the action of the originally gauge-noninvariant model due to Mitra) are investigated under some specific gauge choices in the usual instant form of dynamics (on the hyperplanes x0= constant). The physical contents of the original gauge-noninvariant theory are recovered from that of this gauge-invariant theory under a special choice of gauge, and the quantum equivalence of the two quantized theories is established.PACS Nos.: 03.65+, 03.70+, 11.10lm, 11.10Ef, and 11.30Rd

Gauge-invariant chiral Schwinger model with Faddeevian regularization: Stuckelberg term, operator solution, and Hamiltonian and BRST formulations

A chiral Schwinger model with the Faddeevian regularization a la Mitra is studied in one-space one-time dimension in the conventional form of dynamics (on the hyperplanes x0 = constant) called the “Instant-Form” (IF) dynamics. The original IF theory is seen to be gauge-noninvariant (GNI). Corresponding to this GNI model, a gauge-invariant (GI) theory is constructed through the so-called Stueckelberg term. The operator solution and the Hamiltonian and BRST formulations of the resulting GI theory, obtained by the inclusion of the Stueckelberg term in the action of the original GNI theory, are then investigated with some specific gauge choices. The physical contents of the original GNI theory are also recovered from the newly constructed GI theory under a special gauge.

Interference phenomenon for the Faddeevian regularization of 2D chiral fermionic determinants

The classification of the regularization ambiguity of 2D fermionic determinant in three different classes according to the number of second-class constraints, including the new faddeevian regularization, is examined and extended. We found a new and important result that the faddeevian class, with three second-class constraints, possess a free continuous one parameter family of elements. The criterion of unitarity restricts the parameter to the same range found earlier by Jackiw and Rajaraman for the two-constraints class. We studied the restriction imposed by the interference of right-left modes of the chiral Schwinger model ($\chi QED_{2}$) using Stone's soldering formalism. The interference effects between right and left movers, producing the massive vectorial photon, are shown to constrain the regularization parameter to belong to the four-constraints class which is the only non-ambiguous class with a unique regularization parameter.

Gauge-Invariant Formulation of the Chiral Schwinger Model with Faddeevian Regularization

We introduce the Wess–Zumino field to the chiral Schwinger model with Faddeevian regularization. The Wess–Zumino action has an interesting form; it is a self-dual (chiral) boson action. The Schwinger term between the correctly defined Gauss-law constraints and can be canceled by the WZ action, and the constraint is the first-class one.

Minimal Wess-Zumino-Witten Action and Faddeevian Regularization Scheme in Anomalous D = 2 Non-Abelian Chiral Theory

We discuss anomalous d = 2 non-Abelian chiral theory with minimal Wess–Zumino–Witten (WZW) action. The Schwinger terms between Gauss-law constraints Ga(x) and Gb(y) can not be canceled by the minimal WZW action. If we define modified Gauss-law constraints , the Schwinger terms between the constraints and disappear, the constraints become the first-class ones. And the total action S(A, U, G) is gauge-invariant. When we choose the unitary gauge G = 1, the non-Abelian chiral theory with the generalized faddeevian regularization scheme is gained. And the relation between faddeevian and usual regularization can be obtained.

A NOVEL COVARIANT APPROACH TO THE QUANTIZATION OF INTERACTIVE CHIRAL BOSONS

A new covariant quantization of chiral bosons in the chiral Schwinger model with faddeevian regularization is carried out from Batalin-Fradkin (BF) algorithm. In order to turn the second class chiral constraint into first class constraints, infinitely many BF fields are first introduced. When combined with Batalin-Fradkin-Vilkovisky (BFV) formalism, two kinds of BRST-invariant actions have been derived. The first contains the Wess-Zumino action induced from the usual path-integral approach. But the second includes Wotzasek’s Wess-Zumino action coupled to the gauge fields.

REALIZATION OF THE FADDEEVIAN REGULARIZATION IN AN ANOMALOUS GAUGE THEORY

We analyze the minimal chiral Schwinger model with the Wess-Zumino action in the Hamiltonian formulation and show that Mitra’s “Faddeevian regularization” originates in the matter gauge-fixed model in the case of a regularization ambiguity with a=2. Furthermore, we obtain the generalized model which satisfies the Faddeevian regularization for a≥1.

Relation between Faddeevian and usual regularization in the chiral Schwinger model

We discuss the conventional chiral Schwinger model with the minimal Wess-Zumino action. The Schwinger term between Gauss-law constraints G(x) and G(y) can not be cancelled by the minimal Wess-Zumino action. If we define a modified Gauss-law constraint GM(x), the Schwinger term between the constraints GM(x) and GM(y) disappear. The full action is gauge invariant. When we pick the unitary gauge theta =0, the chiral Schwinger model with the generalized Faddeevian regularization scheme is obtained. The relation between Faddeevian and usual regularization can also be established.

Chiral Schwinger model with a faddeevian regularization

A new solution to the chiral Schwinger model is presented. It is Lorentz invariant, though this is not manifest in the bosonized action. The particle spectrum contains a massive photon and a chiral fermion. The Gauss law commutator exhibits Faddeev's anomaly.