Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

Gauge invariant theories of the generalized chiral Schwinger model

The gauge invariant theories of the generalized chiral Schwinger model are constructed in terms of two schemes with and without Wess-Zumino terms, respectively. Following the former scheme, we calculate the Wess-Zumino term which cancels the gauge anomaly, and then constitute the gauge invariant theory by adding the Wess-Zumino term to the original Lagrangian of the model. According to the latter, we modify the original Hamiltonian by adding a term composed of constraints of the model. It is so designed that the theory described by the modified Hamiltonian and its corresponding first-order Lagrangian maintains gauge invariance. We show by the canonical Dirac method that each of the two gauge invariant theories has the same physical spectrum as that of the original gauge noninvariant formulation.     

Operator solutions of the bosonized chiral Schwinger model

Starting from the modified Lagrangian of the bosonized chiral Schwinger model, operator solutions are obtained under three types of gauge fixing conditions. We show that the physical spectrum consists of a massive free boson and a massless excitation. We emphasize that the “longitudinal” component of the gauge field must be treated properly.     

Geometry and topology of chiral anomalies in gauge theories

Geometrical and topological aspects of chiral anomalies in gauge theories are reviewed. Geometrical and topological concepts and results for chiral anomalies in gauge theories are considered, including differential forms, Lie groups, homotopy, homology, cohomology, Riemannian manifolds, fibre bundles, characteristic classes, index theorems and spectral flow. Gauge theories and their formulation in terms of differential forms and fibre bundles are described. The quantisation of gauge theories is performed using path integrals, and the orbit space, BRST symmetries and ? vacuum are discussed. Gauge theories with fermions are formulated, including realistic models of strong and weak interactions. Chiral anomalies and related issues such as the existence of Schwinger terms, their origins in terms of differential forms, cohomology, the orbit space, BRST identities, Hamiltonian systems and relations to index theorems are analysed. Constraints on models for particle physics from chiral anomalies and theories involving spontaneously broken chiral symmetry described by effective Lagrangians are also mentioned.     

Batalin-Tyutin quantization of the chiral Schwinger model

We quantize the chiral Schwinger model by using the Batalin-Tyutin formalism. We show that one can systematically construct the first-class constraints and the desired involutive Hamiltonian, which naturally generates all secondary constraints. Fora>1, this Hamiltonian gives the gauge invariant Lagrangian including the well-known Wess-Zumino terms, while fora=1 the corresponding Lagrangian has the additional new type of the Wess-Zumino terms, which are irrelevant to the gauge symmetry.     

The Relation Between Gauge and Non-Gauge Abelian Models

This work studies the relationship between gauge-invariant and non gauge-invariant Abelian vector models. Following a technique introduced by Harada and Tsutsui, we show that the Proca and the chiral Schwinger models may both be viewed as gauge-fixed versions of genuinely gauge-invariant models. This leads to the proposal that any consistent Abelian vector model with no gauge symmetry can be understood as a gauge theory that had its gauge fixed, which establishes an equivalence between gauge-invariant and non gauge-invariant models. Finally, we show that a gauge-invariant version of the chiral Schwinger model, after integrating out the fermionic degrees of freedom, can be identified with the two-dimensional Stueckelberg model without the gauge-fixing term.     

On the Gauge and BRST Invariance of the Chiral QED with Faddeevian Anomaly

Chiral Schwinger model with the Faddeevian anomaly is considered. It is found that imposing a chiral constraint this model can be expressed in terms of chiral boson. The model when expressed in terms of chiral boson remains anomalous and the Gauss law of which gives anomalous Poisson brackets between itself. In spite of that a systematic BRST quantization is possible. The Wess-Zumino term corresponding to this theory appears automatically during the process of quantization. A gauge invariant reformulation of this model is also constructed. Unlike the former one gauge invariance is done here without any extension of phase space. This gauge invariant version maps onto the vector Schwinger model. The gauge invariant version of the chiral Schwinger model for a=2 has a massive field with identical mass however gauge invariant version obtained here does not map on to that.     

Chiral Bosonized Versions Hidden in Chiral Schwinger Models

The left- and right-handed chiral Schwinger models are re-examined by a modified chiral bosonization. Contrary to the usual chiral bosonization, we impose the chiral constraint on the right-handed chiral Schwinger model and the antichiral constraint on the left-handed one. The resulting chiral boson and theories are gauge-invariant and equivalent to one (free) cbiral boson and one antichiral boson respectively.     

Chiral Schwinger model with new regularization

A recently proposed version of the chiral Schwinger model is studied in detail in this paper. It is shown that a suitable Pauli-Villars regularization can be devised to reproduce the bosonized form of the effective action that was earlier written down. It is then shown how this anomalous gauge theory can be made gauge invariant by the introduction of a Wess-Zumino field. The equations of motion of this theory are explicitly solved in Lorentz covariant gauges. Finally, the operator solution of the fermionic form of the theory is constructed.     

Perturbation theory in terms of superfields and its application to gauge theories

We formulate a perturbation theory in terms of superfields for Lagrangian field theories which are expressable by chiral or general scalar superfields. Especially we consider the generalized QED model of Wess and Zumino where an additional local gauge symmetry is present. Our calculations are manifestly covariant with respect to supersymmetry and local gauge transformations.     

Chiral Schwinger model with a Podolsky term at finite temperature

We study an exactly solvable two-dimensional model which mimics the basic features of the standard model. This model combines chiral coupling with an infrared behavior which resembles low energy QCD. This is done by adding a Podolsky higher-order derivative term in the gauge field to the Lagrangian of the usual chiral Schwinger model. We adopt a finite temperature regularization procedure in order to calculate the non-trivial fermionic Jacobian and obtain the photon and fermion propagators, first at zero temperature and then at finite temperature in the imaginary and real time formalisms. Both singular and non-singular cases, corresponding to the choice of the regularization parameter, are treated. In the nonsingular case there is a tachyonic mode as usual in a higher order derivative theory, however in the singular case there is no tachyonic excitation in the spectrum.     

New Terms for Compact Form of Electroweak Chiral Lagrangian

The compact form of the electroweak chiral Lagrangian is a reformulation of its original form and is expressed in terms of chiral rotated electroweak gauge fields, which is crucial for relating the information of underlying theories to the coefficients of the low-energy effective Lagrangian. However the compact form obtained in previous works is not complete. In this letter we add several new chiral invariant terms to it and discuss the contributions of these terms to the original electroweak chiral Lagrangian.     

Vector boson mass generation in two dimensions

Gauge theories in two dimensions generate masses for the gauge bosons via the Schwinger mechanism. This mechanism is studied in two models based on a direct product group gauge invariance. The gauge boson mass spectrum is determined in each case.     

Gauge invariant Lagrangian construction for massive higher spin fermionic fields

We formulate a general gauge invariant Lagrangian construction describing the dynamics of massive higher spin fermionic fields in arbitrary dimensions. Treating the conditions determining the irreducible representations of Poincaré group with given spin as the operator constraints in auxiliary Fock space, we built the BRST charge for the model under consideration and find the gauge invariant equations of motion in terms of vectors and operators in the Fock space. It is shown that like in massless case [I.L. Buchbinder, V.A. Krykhtin, A. Pashnev, Nucl. Phys. B 711 (2005) 367, hep-th/0410215], the massive fermionic higher spin field models are the reducible gauge theories and the order of reducibility grows with the value of spin. In compare with all previous approaches, no off-shell constraints on the fields and the gauge parameters are imposed from the very beginning, all correct constraints emerge automatically as the consequences of the equations of motion. As an example, we derive a gauge invariant Lagrangian for massive spin 3/2 field.     

Variational Study of 〈ψψ〉 in the Lattice Schwinger Model with Wilson Fermions

We used the variational method in lattice gauge theory to calculate the chiral order parameter 〈ψψ〉 in the Schwinger model with Wilson fermions.     

Lorentz invariant exact solution of the anomalous chiral Schwinger model

We present an exact solution of the anomalous chiral Schwinger model using Fermionic variables. We implement infrared regularization by considering the model on a spatial circleS ¹. Quantum effects modify the gauge constraints through the appearance of Schwinger terms in the gauge algebra. We perform a careful analysis of the resulting second class gauge constraints by implementing Dirac's method at the quantum level and obtain the spectrum of the theory. We get a consistent unitary Lorentz invariant theory for particular values of the counterterms. We find that when we regulate the fermionic sector of the model without reference to the gauge fields Lorentz invariance requires that we add both Lorentz variant and gauge variant counterterms.     

Phase factors,point-splitting regularisation and chiral anomalies

A method is proposed to construct the path-independent form of phase factors pertaining to non-abelian gauge theories. It is found that the original form of the phase factor, as envisaged by Schwinger, is reproduced for a straight path. As an illustration of its use this work is applied, within the framework of point-splitting regularisation, to obtain the familiar axial anomaly in a pure vector gauge theory. Subtleties associated with the treatment of the vector gauge current are also discussed. Finally, the scheme of computations is employed to derive the covariant and consistent anomalies in a non-abelian chiral gauge theory in arbitrary even dimensions.     

Physical variables in gauge theories

The symplectic method is applied to obtain the physical variables and the physical Hamiltonian in two examples of gauge theories: the electrodynamics in the Coulomb gauge and the two-dimensional bosonic Schwinger model.     

Quantization of Two Classical Models by Means of the BRST Quantization Method

An elementary gauge-non-invariant model and the bosonized form of the chiral Schwinger model are introduced as classical theories. The constraint structure is then investigated. It is shown that by introducing a new field, these models can be made gauge-invariant. The BRST form of quantization is reviewed and applied to each of these models in turn such that gauge-invariance is not broken. Some consequences of this form of quantization are discussed.