Fermionic representation of the Wess-Zumino term and the chiral Schwinger model

The quantum structure of the chiral Schwinger model is studied by fermionization of the Wess-Zumino field. The model contains a hidden parameter a reflecting the ambiguity in the definition of the gauge anomaly. It is shown that, for the special value a = 2, this chiral model is equivalent to massless QED₂ in the sence that they share the same gauge field and the same (left-handed) chiral fermion. The fermionic representation of the Wess-Zumino term provides a natural way to summarize the current algebras and yields a regularization-independent current-algebraic characterization of the model.     

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.     

The Wess-Zumino term for supermembranes and descent equations

As a result of the Wess-Zumino term in its action, the eleven-dimensional supermembrane realizes the super-Poincaré algebra extended by a Schwinger term containing a two-form charge. A set of “descent equations” are determined which place the relationship between the Wess-Zumino Lagrangian and the Schwinger term on a cohomological footing.     

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.     

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.     

Hamiltonian quantization of the non-anomalous generalized Schwinger model

We quantize a generalized version of the Schwinger model, where the two chiral sectors couples with different strengths to theU(1) gauge field. Starting from a theory which includes a generalized Wess-Zumino term, we obtain the equal time commutation relation for physical fields, both the singular and non-singular cases are considered. The photon propagators are also computed in their gauge dependent and invariant versions.     

Perturbation theory for the anomaly-free chiral Schwinger model

We apply perturbation theory to the gauge invariant version of the chiral Schwinger model. The cancellation of anomalies is shown explicitly in terms of Feynman diagrams. We calculate the exact propagators for the gauge field, for the Wess-Zumino field and for the mixing between these fields. Using these propagators, we demonstrate the existence of a massive state.     

Minimal Wess-Zumino-Witten Act ion 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 G^a(x) and G^b(y) can not be canceled by the minimal WZW action. If we define modified Gauss-law constraints G_m^a(x), the Schwinger terms between the constraints G_m^a(x) and G_m^b(y) disappear, the constraints G_m^a(x) become the first-class ones. And the total action S(A, U, G) is gaugeinvariant. 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.     

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.     

Derivation of the Wess-Zumino action for the generalized Schwinger model from the Batalin-Fradkin algorithm

We apply the Batalin-Fradkin algorithm combined with the Batalin-Fradkin-Vilkovisky formalism to the generalized Schwinger model. We obtain the Becchi-Rouet-Stora-Tyutin invariant action showing that the auxiliary fields introduced in the algorithm turn into the Wess-Zumino scalar.     

ANOMALIES,COHOMOLOGY AND ChIERN-SIMONS COCHAINS

We present a concept of the gauge transformations, establish the homomorphic relation between this conomology group and the Chern-Simons type. charaateric class sequence,and analyse their applacatons to the non-Abelian anomaly, the gauge invariant Wess-Zumino effective action and the Schwinger term etc.we show that the present approaches.includes faddeev's song's and zumino'sapproaches.     

反常、Chern-Simons上链

本文提出一种联络空间上同调的概念,建立这种上同调群与Chern-Simons型示性类系列的同态关系,给出它们在反常、Wess-Zumino有效作用与Schwinger项等问题上的应用;从而概括了Faddeev,宋行长,Zumino等人最近关于这些问题的探讨。 关键词：     

Anomalous current algebras in the Skyrme model or chiral G×G with Wess-Zumino term

We deal with chiral G×G field theory with Wess-Zumino term (or the Skyrme model) specified in terms of its Goldstone fields. Working in four dimensions we derive the current of the Noether currents of the theory in the canonical formalism displaying its anomalous structure.     

Microscopically derived Wess-Zumino action for 3He-A

It is shown that the effective action in ³He-A contains the Wess-Zumino topological action, from which the orbital dynamics is naturally obtained. The obtained spontaneous orbital momentum of liquid coincides fully with the one predicted by phenomenology. The connection with the chiral anomaly in quantum electrodynamics is considered.     

Global aspects of current algebra

A new mathematical framework for the Wess-Zumino chiral effective action is described. It is shown that this action obeys an a priori quantization law, analogous to Dirac's quantization of magnetic change. It incorporates in current algebra both perturbative and non-perturbative anomalies.     

Interacting Theory of Chiral Bosons and Gauge Fields on Noncommutative Extended Minkowski Spacetime

Several interacting models of chiral bosons and gauge fields are investigated on the noncommutative extended Minkowski spacetime which was recently proposed from a new point of view of disposing noncommutativity. The models include the bosonized chiral Schwinger model, the generalized chiral Schwinger model (GCSM) and its gauge invariant formulation. We establish the Lagrangian theories of the models, and then derive the Hamilton's equations in accordance with the Dirac's method and solve the equations of motion, and further analyze the self-duality of the Lagrangian theories in terms of the parent action approach.     

Wess-Zumino Effective Action on a Lattice

Taking Wilson fermion formulation for the chiral gauge theory we derive the Wess-Zumino effective action in a lattice version in both two and four dimensions. Also the relationship between the anomalous generation and the chiral symmetry breaking is presented. Our results in continuum limit are coincident with those obtained by other regularizations.     

BRST-BFV formalism for the generalized Schwinger model

We derive the Wess-Zumino scalar term of the generalized Schwinger model both in the singular and nonsingular cases by using BRST-BFV framework. The photon propagators are also computed in the extended Lorentz gauge.     

On the exchange matrix for WZNW model

The connection between the exchange algebra in theSU(2) Wess-Zumino Novikov-Witten model and the quantum groupSU(2) is discussed. It is shown that on the quasiclassical level this connection has the simple interpretation in terms of the Lie-Poisson action ofSU(2) on the chiral components of the fields in the WZNW model.Dedicated to Res Jost and Arthur Wightman