Vector Schwinger Model Research Articles

On the indistinguishability of chiral QED with parameter-free Faddeevian anomaly and QED under a chiral constraint

We carry out an investigation imposing a chiral constraint in the phase space of vector and axial-vector Schwinger model. We find that resulting models become identical to a gauge non-invariant model which was obtained by the imposition of chiral constraint in the phase space of in Chiral Schwinger model with the parameter-free Faddeevian anomaly. Three different models having different types of interaction between the matter and gauge field become indistinguishable under a chiral constraint at the quantum mechanical level. The resulting gauge non-invariant model has an equivalent gauge-invariant version in the same phase space that can be identified with the vector Schwinger model.

On augmented superfield approach to vector Schwinger model

We exploit the techniques of Bonora–Tonin superfield formalism to derive the off-shell nilpotent and absolutely anticommuting (anti-)BRST as well as (anti-)co-BRST symmetry transformations for the (1[Formula: see text]+[Formula: see text]1)-dimensional (2D) bosonized vector Schwinger model. In the derivation of above symmetries, we invoke the (dual)-horizontality conditions as well as gauge and (anti-)co-BRST invariant restrictions on the superfields that are defined onto the (2,[Formula: see text]2)-dimensional supermanifold. We provide geometrical interpretation of the above nilpotent symmetries (and their corresponding charges). We also express the nilpotency and absolute anticommutativity of the (anti-)BRST and (anti-)co-BRST charges within the framework of augmented superfield formalism.

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.

Light-Front BRST Quantization of the Vector Schwinger Model with a Photon Mass Term

Vector Schwinger model with a mass term for the photon, describing 2D electrodynamics with mass-less fermions, studied by us recently (UK, Mod. Phys. Lett A22, 2993 (2007), PoS LC2008, 008 (2008), UK and DSK, Int. J. Mod. Phys. A22, 6183 (2007), UK, Mod. Phys. Lett A27, 1250157 (2012)), represents a new class of models. This theory becomes gauge-invariant when studied on the light-front. This is in contrast to the instant-form theory which is gauge-non-invariant. The light-front Hamiltonian and path integral quantization of this theory has been studied recently by one of us (UK, Mod. Phys. Lett. A27 (No. 27) 1250157 (2012)). In the present work we study the light-front Becchi-Rouet-Stora and Tyutin (BRST) quantization of this theory under appropriate light-cone BRST gauge-fixing. Here the BRST (gauge) symmetry of the theory is maintained even under BRST-gauge-fixing which is in contrast to its Hamiltonian and path integral quantization where the gauge symmetry of the theory necessarily gets broken under gauge-fixing.

Novel symmetries in vector Schwinger model

We derive nilpotent and absolutely anticommuting (anti-)co-BRST symmetry transformations for the bosonized version of (1+1)-dimensional (2D) vector Schwinger model. These symmetry transformations turn out to be the analog of co-exterior derivative of differential geometry as the total gauge-fixing term remains invariant under it. The exterior derivative is realized in terms of the (anti-)BRST symmetry transformations of the theory whereas the bosonic symmetries find their analog in the Laplacian operator. The algebra obeyed by these symmetry transformations turns out to be exactly same as the algebra obeyed by the de Rham cohomological operators of differential geometry.

LIGHT-FRONT HAMILTONIAN AND PATH INTEGRAL QUANTIZATION OF VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM

Vector Schwinger model with a mass term for the photon, describing 2D electrodynamics with massless fermions, studied by us recently [U. Kulshreshtha, Mod. Phys. Lett. A22, 2993 (2007); U. Kulshreshtha and D. S. Kulshreshtha, Int. J. Mod. Phys. A22, 6183 (2007); U. Kulshreshtha, PoS LC2008, 008 (2008)], represents a new class of models. This theory becomes gauge-invariant when studied on the light-front. This is in contrast to the instant-form theory which is gauge-non-invariant. In this work, we study the light-front Hamiltonian and path integral quantization of this theory under appropriate light-cone gauge-fixing. The discretized light-cone quantization of the theory where we wish to make contact with the experimentally observational aspects of the theory would be presented in a separate paper.

MOMENTUM SPACE REGULARIZATIONS AND THE INDETERMINACY IN THE SCHWINGER MODEL

We revisited the problem of the presence of finite indeterminacies that appear in the calculations of a Quantum Field Theory. We investigate the occurrence of undetermined mathematical quantities in the evaluation of the Schwinger model in several regularization scenarios. We show that the undetermined character of the divergent part of the vacuum polarization tensor of the model, introduced as an ansatz in previous works, can be obtained mathematically if one introduces a set of two parameters in the evaluation of these quantities. The formal mathematical properties of this tensor and their violations are discussed. The analysis is carried out in both analytical and sharp cutoff regularization procedures. We also show how the Pauli–Villars regularization scheme eliminates the indeterminacy, giving a gauge invariant result in the vector Schwinger model.

GAUGE-INVARIANT REFORMULATION OF THE VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM AND ITS HAMILTONIAN, PATH INTEGRAL AND BRST FORMULATIONS

Using the Stueckelberg formalism, we construct a gauge-invariant version of the vector Schwinger model (VSM) with a photon mass term studied by one of us recently. This model describes two-dimensional massive electrodynamics with massless fermions, where the left-handed and right-handed fermions are coupled to the electromagnetic field with equal couplings. This model describing the 2D massive electrodynamics becomes gauge-noninvariant (GNI). This is in contrast to the case of the massless VSM which is a gauge-invariant (GI) theory (as a consequence of demanding the regularization for the theory to be GI). In this work we first construct a GI theory corresponding to this model describing the 2D massive electrodynamics, using the Stueckelberg formalism and then we recover the physical contents of the original GNI theory studied earlier, under some special gauge choice. We then study the Hamiltonian, path integral and BRST formulations of this GI theory under appropriate gauge-fixing. The theory presents a new class of models in the 2D quantum electrodynamics with massless fermions but with a photon mass term.

VECTOR SCHWINGER MODEL WITH A PHOTON MASS TERM: GAUGE-INVARIANT REFORMULATION, OPERATOR SOLUTIONS AND HAMILTONIAN AND PATH INTEGRAL FORMULATIONS

We consider the vector Schwinger model (VSM) describing two-dimensional electrodynamics with massless fermions, where the left-handed and right-handed fermions are coupled to the electromagnetic field with equal couplings, with a mass term for the U(1) gauge field and then study its operator solutions and the Hamiltonian and path integral formulations. We emphasize here that although the VSM has been studied in the literature rather widely but only without a photon mass term (which was a consequence of demanding the regularization for the VSM to be gauge-invariant (GI)). The VSM with a photon mass term is seen to be a gauge-noninvariant (GNI) theory. Using the standard Stueckelberg formalism we then construct a GI theory corresponding to the proposed GNI model. From this reformulated GI theory, we further recover the physical contents of the proposed GNI theory under a very special gauge choice. The theory proposed and studied here presents a new class of models in the two-dimensional quantum electrodynamics with massless fermions but with a photon mass term.

Restrictions over two-dimensional gauge models with Thirring-like interaction

Some years ago, it was shown how fermion self-interacting terms of the Thirring-type impact the usual structure of massless two-dimensional gauge theories [1]. In that work only the cases of pure vector and pure chiral gauge couplings have been considered and the corresponding Thirring term was also pure vector and pure chiral respectively, such that the vector (or chiral) Schwinger model should not lose its chirality structure due to the addition of the quartic interaction term. Here we extend this analysis to a generalized vector and axial coupling both for the gauge interaction and the quartic fermionic interactions. The idea is to perform quantization without losing the original structure of the gauge coupling. In order to do that we make use of an arbitrariness in the definition of the Thirring-like interaction.

Structural Aspects of Two-Dimensional Anomalous Gauge Theories

A foundational investigation of the basic structural properties of two-dimensional anomalous gauge theories is performed. The Hilbert space is constructed as the representation of the intrinsic local field algebra generated by the fundamental set of field operators whose Wightman functions define the model. We examine the effect of the use of a redundant field algebra in deriving basic properties of the models and show that different results may arise, as regards the physical properties of the generalized chiral model, in restricting or not the Hilbert space as a representation of the intrinsic local field algebra. The question of whether the vector Schwinger model is a limit of the generalized anomalous model is also discussed. We show that this limit can only be consistently defined for a field subalgebra of the generalized model.

To Restore the Broken Symmetry in the Nonconfining Schwinger Model

A new generalization of the vector Schwinger model is considered where gauge symmetry is broken at the quantum mechanical level. By proper extension of the phase space this broken symmetry has been restored in two different ways. One of these two leads to a BRST-invariant effective action. An equivalent gauge-invariant theory is reformulated even in the usual phase space also.

Algebraic Isomorphism in Two-Dimensional Anomalous Gauge Theories

The operator solution of the anomalous chiral Schwinger model is discussed on the basis of the general principles of Wightman field theory. Some basic structural properties of the model are analyzed taking a careful control on the Hilbert space associated with the Wightman functions. The isomorphism between gauge noninvariant and gauge invariant descriptions of the anomalous theory is established in terms of the corresponding field algebras. We show that (i) theΘ-vacuum representation and (ii) the suggested equivalence of vector Schwinger model and chiral Schwinger model cannot be established in terms of the intrinsic field algebra

Domain wall fermions and MC simulations of vector theories

It is known that domain wall fermions may be used in MC simulations of vector theories. The practicality and usefulness of such an implementation is investigated in the context of the vector Schwinger model, on a 2+1 dimensional lattice. Preliminary results of a Hybrid Monte Carlo simulation are presented.

Some applications of the overlap formalism

The massless vector Schwinger model with $N_f=1,2,3,4$ number of flavors is studied on the lattice using the overlap formalism. A full Monte Carlo simulation yields values for the bilinear fermion condensate that are in agreement with the exact solution of the continuum Schwinger model with an added Thirring interaction.

The generalized chiral Schwinger model on the two-sphere

A family of theories which interpolate between vector and chiral Schwinger models is studied on the two-sphere S 2. The conflict between the loss of gauge invariance and global geometrical properties is solved by introducing a fixed background connection. In this way the generalized Dirac-Weyl operator can be globally defined on S 2. The generating functional of the Green functions is obtained by taking carefully into account the contribution of gauge fields with non-trivial topoligical charge and of the related zero-modes of the Dirac determinant. In the decompactification limit, the Green functions of the flat case are recovered; in particular the fermionic condensate in the vacuum vanishes, at variance with its behaviour in the vector Schwinger model.

COMMENT ON MASS GENERATION IN THE CHIRAL SCHWINGER MODEL

The mass generation mechanism for the gauge boson in the chiral Schwinger model is compared with one in the vector Schwinger model. They do not differ substantially, and we argue that an anomalous chiral gauge theory should be seen generally as a special low-energy version of a gauge invariant theory.

θ VACUUM IN THE CHIRAL SCHWINGER MODEL

The physical properties of the chiral Schwinger model are studied, for the particular value of the regularization-dependent parameter a=2. Within a gauge-invariant formulation, we prove that, apart from free physical chiral states, the chiral Schwinger model is equivalent to the vector Schwinger model. In particular, we show that, as in the vector theory, the cluster property is not fulfilled unless the vacuum state is properly defined.