Wess-Zumino Fields Research Articles

On the Poincaré and Gauge Symmetry of a Model where Vector and Axial Vector Interaction get Mixed up with Different Weight

A $(1+1)$ dimensional model where vector and axial vector interaction get mixed up with different weight is considered with a generalized masslike term for gauge field. Through Poincar\'e algebra it has been made confirm that only a Lorentz covariant masslike term leads to a physically sensible theory as long as the number of constraints in the phase space is two. With that admissible masslike term, phase space structure of this model with proper identification of physical canonical pair has been determined using Diracs' scheme of quantization of constrained system. The bosonized version of the model remains gauge non-invariant to start with. Therefore, with the inclusion of appropriate Wess-Zumino term it is made gauge symmetric. An alternative quantization has been carried out over this gauge symmetric version to determine the phase space structure in this situation. To establish that the Wess-Zumino fields allocates themselves in the un-physical sector of the theory an attempts has been made to get back the usual theory from the gauge symmetric theory of the extended phase-space without hampering any physical principle. It has been found that the role of gauge fixing is crucial for this transmutation.

Instant-Form and Light-Front Hamiltonian and Path Integral Formulations of the Conformally Gauge-Fixed Polyakov D1-Brane Action in the Presence of a Scalar Axion Field and an <i>U</i>(1) Gauge Field

Recently we have studied the instant-form quantization (IFQ) and the light-front quantization (LFQ) of the conformally gauge-fixed Polyakov D1 brane action using the Hamiltonian and path integral formulations. The IFQ is studied in the equal world-sheet time framework on the hyperplanes defined by the world-sheet time σ0=τ=constant and the LFQ in the equal light-cone world-sheet time framework, on the hyperplanes of the light-front defined by the light-cone world-sheet time σ+= (τ+σ) =constant. The light-front theory is seen to be a constrained system in the sense of Dirac in contrast to the instant-form theory. However, owing to the gauge anomalous nature of these theories, both of these theories are seen to lack the usual string gauge symmetries defined by the world-sheet reparametrization invariance (WSRI) and the Weyl invariance (WI). In the present work we show that these theories when considered in the presence of background gauge fields such as the NSNS 2-form gauge field Bαβ(σ,τ) or in the presence of U(1) gauge field Aα(σ,τ) and the constant scalar axion field C(σ,τ), then they are seen to possess the usual string gauge symmetries (WSRI and WI). In fact, these background gauge fields are seen to behave as the Wess-Zumino or Stueckelberg fields and the terms containing these fields are seen to behave as Wess-Zumino or Stueckelberg terms for these theories.

Formulation and quantization of a generalized model related to the chiral Schwinger model

A generalized theory which describes fermions interacting with a gauge field is investigated. In 1 + 1 dimensions such a model is equivalent to a theory in which a boson field appears in the Lagrangian density rather than a fermion field. In this form, the Lagrangian density can be diagonalized and then quantized in terms of the transformed fields. The case of the chiral Schwinger model can be obtained from the general model and the physics with respect to the operator form is discussed. It is shown how the theory can be made nonanomalous by means of a Wess–Zumino field.

Removing the Wess Zumino fields in the BFFT formalism

In this paper we give some prescriptions in order to remove the Wess Zumino fields of the BFFT formalism and, consequently, we derive a gauge invariant system written only in terms of the original second class phase space variables. Here, the Wess Zumino fields are considered only as auxiliary variables that permit us to reveal the underlying symmetries present in a second class system. We apply our formalism in three important and illustrative constrained systems which are the Chern Simons Proca theory, the Abelian Proca model and the reduced SU(2) Skyrme model.

GAUGING BY SYMMETRIES

We propose a new procedure to embed second class systems by introducing Wess–Zumino (WZ) fields in order to unveil hidden symmetries existent in the models. This formalism is based on the direct imposition that the new Hamiltonian must be invariant by gauge-symmetry transformations. An interesting feature in this approach is the possibility to find a representation for the WZ fields in a convenient way, which leads to preserve the gauge symmetry in the original phase space. Consequently, the gauge-invariant Hamiltonian can be written only in terms of the original phase-space variables. In this situation, the WZ variables are only auxiliary tools that permit to reveal the hidden symmetries present in the original second class model. We apply this formalism to important physical models: the reduced-SU(2) Skyrme model, the Chern–Simons–Proca quantum mechanics and the chiral bosons field theory. In all these systems, the gauge-invariant Hamiltonians are derived in a very simple way.

Structural Aspects of the Fermion-Boson Mapping in Two-Dimensional Gauge and Anomalous Gauge Theories with Massive Fermions

Using a synthesis of the functional integral and operator approaches we discuss the fermion-boson mapping and the role played by the Bose field algebra in the Hilbert space of two-dimensional gauge and anomalous gauge field theories with massive fermions. In QED2 with quartic self-interaction among massive fermions, the use of an auxiliary vector field introduces a redundant Bose field algebra that should not be considered as an element of the intrinsic algebraic structure defining the model. In anomalous chiral QED2 with massive fermions the effect of the chiral anomaly leads to the appearance in the mass operator of a spurious Bose field combination. This phase factor carries no fermion selection rule and the expected absence of Θ-vacuum in the anomalous model is displayed from the operator solution. Even in the anomalous model with massive Fermi fields, the introduction of the Wess–Zumino field replicates the theory, changing neither its algebraic content nor its physical content.

On the origin of divergences in massless QED2

We show that ultraviolet divergences found in fermionic Green functionsof massless QED2 have an essentially non-perturbative nature. Weinvestigate their origin both in the gauge invariant formalism (wherewe introduce Wess-Zumino fields to restore quantum gauge invariance)and in the gauge non-invariant formalism, mapping two different butequivalent mechanisms responsible for their appearance. We find the sameresults in both approaches, what contradicts a previous work of Jian-Ge,Qing-Hai and Yao-Yang, that found no divergences in the chiral Schwingermodel considered in the gauge invariant formalism.

Polyakov conjecture on the supertorus

We prove the Polyakov conjecture on the supertorus (ST2): We determine an iterative solution at any order of the superconformal Ward identity and we show that the Polyakov action that describes the (1,0) 2D(two-dimensional)-supergravity, resums this perturbative series. The resolution of the super-Beltrami equation for the Wess–Zumino field from which the Polyakov action is expressed, is done by using on the one hand the Cauchy kernel techniques on ST2 defined in H. Kachkachi and M. Kachkachi, Class. Quantum Grav. 11, 493 (1994) and on the other hand, the formalism developed in M. Kachkachi and S. Kouadik, J. Math. Phys. 38, 4336 (1997). Hence, we determine the n-points Green functions from the Polyakov action expressed as a functional integral of the Beltrami superfield μ̂.

Axial and Gauge Anomalies in the BV Formalism

We discuss the quantization of the Schwinger and the axial Schwinger models in the Batalin–Vilkovisky–Lagrangian framework in order to illustrate how the one-loop order corrections to the action can be chosen in such a way that we may have either the vector current or the axial current conserved. We show for these two models that a BRST invariant local representation can be obtained by introducing extra Wess–Zumino fields. We also discuss the choice of the regulating operator, including the case of the chiral Schwinger model.

A covariant approach to gauged 2D self-dual fields

It is shown that the chiral boson model of Floreanini and Jackiw (FJ) and of MClain, Wu and Yu (MWY) are two different representations of the same chiral theory, each displaying different aspects of the bosonic representation for chiral fields: while in the FJ side the spectrum is quite evident from the equations of motion, it lacks manifest covariance making the coupling to external fields particularly difficult. On the MWY side, a symmetry hidden in the FJ version is apparent due to the presence of infinite scalar Wess-Zumino fields that carry the chiral representation in this side of the problem. On the other hand the evidence of physical spectrum is lost. In this work we show how to go from one representation to the other and find that the FJ chiral field is a collective field built by a linear combination of all MWY scalar fields. Using then the manifest covariance of the MWY representation we study the problem of coupling bosonic chiral fields to a background gauge field.

On the covariantization of the chiral constraints

We show that a complete covariantization of the chiral constraint in the Floreanini-Jackiw necessitates an infinite number of auxiliary Wess-Zumino fields other-wise the covariantization is only partial and unable to remove the nonlocality in the chiral boson operator. We comment on recent works that claim to obtain covariantization through the use of Batalin-Fradkin-Tyutin method, that uses just one Wess-Zumino field.

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.

Construction of the BRST-Invariant Action for a Gauged Self-Dual Theory by Making Use of the Batalin-Fradkin Algorithm11The project supported by the Grant LWTZ-1298 of the Chinese Academy of Sciences

The Batalin–Fradkin algorithm combined with the Batalin–Fradkin–Vilkovisky formalism is applied to a two-dimensional model of a self-dual field interacting chirally with a gauge field. A Becchi–Rouet–Stora–Tyutin gauge-fixing action is obtained with auxiliary fields introduced in the algorithm turning into a Wess–Zumino field. The chirality of the Wess-Zumino field appears in a natural way.

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.

Alternative gauge-invariant formulation of the generalized Schwinger model

The Mitra-Rajaraman method, which involves no Wess-Zumino fields, is applied to construct a gauge-invariant formulation of the generalized Schwinger model. It is shown that the gauge-invariant and the gauge-non-invariant versions of the model have the same physical content.

On the hidden U(1) gauge symmetry in the nonlinear sigma model

As shown by Kovner and Rosenstein, the O(N) invariant nonlinear sigma model, which in Dirac’s language of constrained systems presents only second-class type of constraints, possess a hidden U(1) gauge symmetry. The presence of this symmetry is investigated, in this work, with the introduction of a Wess–Zumino term that implements Faddeev’s idea of changing second-class constraints into gauge generating first-class constraints. The resulting theory exhibits the embedding of the O(N) invariant model into a gauge theory which presents an enlarged phase-space with the inclusion of a Wess–Zumino field.

Minimal chiral Schwinger model in the matter gauge

In the gauge-invariant formulation of the minimal chiral Schwinger model, we explicitly show the role of the Wess–Zumino field, which seems to be dynamical in the matter gauge φL=0. Furthermore, in this gauge we show how the left-handed chirality is maintained in the physical Hilbert space.

NON-ANOMALOUS BOSONIZED THEORIES FROM A GAUGE PRINCIPLE

Starting with a gauge principle for a scalar boson we show that one can get, in 1+1 dimensions, the Lagrangian density of the generalized Schwinger model (GSM) in its bosonized version. This occurs for a particular value of the regularization parameter. Then we show how to get the model with the arbitrary parameter through the introduction of the Wess-Zumino field. Finally we study the possible extension of this procedure to higher dimensions, particularly to 2+1 dimensions.

A Note on the Regularization Parameter a of Non-Abelian Chiral Theory in Two Dimensions11The project supported by the special foundation for doctoral training of the National Education Committee of China under Grant No. 9035805

The renormalisation properties of non-Abelian chiral Schwinger model is studied. The one loop renormalixation counterterm is calculated. The results show that a (an arbitrary parameter appearing in the theory and determining its unitarity) is renormalized unless it is equal to zero or two, and there is neither coupling constant renormalization of e nor wave function renormalization of gauge field, fermion field, and Wess-Zumino field.

Consistency and current algebras of a non-Abelian chiral gauge theory in four dimensions.

We present a gauge-symmetric reformulation of anomalous gauge theories and study the symmetry structures of an $\mathrm{SU}(N)$ chiral gauge model in four dimensions. The gauge symmetry is made manifest via the introduction of the Wess-Zumino term, but turns out to be spontaneously broken; correspondingly, the gauge bosons become massive and some nonstandard self-interactions of gauge bosons arise. While the total gauge current, consisting of both fermion and unphysical Wess-Zumino fields, is anomaly free, the gauge anomalies and the Schwinger terms reappear in the fermion chiral currents and are related through the underlying gauge symmetry. Canonical reasoning is given to establish their connection.