A gauge-invariant theory of chiral bosons: Wess-Zumino term,Hamiltonian and BRST formulations

The Wess-Zumino term for the gauge-non-invariant Srivastava model for single self-dual chiral bosons is constructed, and the Hamiltonian and BRST formulations of the resulting gauge-invariant theory (obtained by the inclusion of the Wess-Zumino term) are investigated.     

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.     

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.     

Solutions of theU(N)σ models with the Wess-Zumino term

We study finite action classical solutions of the Euclidean two-dimensionalU(N) sigma models with the Wess-Zumino term. We show that these solutions are related to (and so can be derived from) the solutions of the Lax-pair problem for the correspondingU(N) sigma model (without the Wess-Zumino term). We discuss the value of the action for these solutions and prove that all these solutions are unstable.     

Solutions of theU(N)σ models with the Wess-Zumino term

We study finite action classical solutions of the Euclidean two-dimensionalU(N) sigma models with the Wess-Zumino term. We show that these solutions are related to (and so can be derived from) the solutions of the Lax-pair problem for the correspondingU(N) sigma model (without the Wess-Zumino term). We discuss the value of the action for these solutions and prove that all these solutions are unstable.     

The Wess-Zumino term in lattice theories

The chiral property of the Wilson lattice fermion is investigated. A chiral-invariant four-Fermi model, in which chiral symmetry is dynamically broken, is considered in 2 and 4 dimensions. The Wess-Zumino term is calculated in the 1/N_c expansion. In 2 dimensions, the Wess-Zumino term appears from the Wilson term in the desired form. However, in 4 dimensions the mass-independent one does not appear. The physical reason for this result is discussed.     

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 G(Χ) and G(y) can be canceled by the WZ action, and the constraint G(Χ) is the first-class one.     

Holonomy and the Wess-Zumino term

The concept of a holonomy term in a Lagrangian is introduced. It unifies the idea of the interaction term in the Dirac monopole and the Wess-Zumino term. In particular, it provides a dynamical interpretation of the Kac-Moody cocycle on a loop group.     

Nuclear effects on the structure functions

We calculate the branching ratio for the semihadronic decay τ→ηππν, a test fo the Wess-Zumino term for chiral anomalies.     

Unoriented WZW Models and Holonomy of Bundle Gerbes

The Wess-Zumino term in two-dimensional conformal field theory is best understood as a surface holonomy of a bundle gerbe. We define additional structure for a bundle gerbe that allows to extend the notion of surface holonomy to unoriented surfaces. This provides a candidate for the Wess-Zumino term for WZW models on unoriented surfaces. Our ansatz reproduces some results known from the algebraic approach to WZW models. manche meinen lechts und rinks kann man nicht velwechsern werch ein illtum Ernst Jandl [Jan95] K.W. is supported with scholarships by the German Israeli Foundation (GIF) and by the Rudolf und Erika Koch–Stiftung.     

Associativity in Wess-Zumino model and Kac-Moody algebra

Topological quantization of the coefficient of the Wess-Zumino model is investigated in Hamilton formalism. Quantization is shown to be required from the associativity of the operators. Center of the Kac-Moody algebra is also quantized from the requirement of the associativity. We show that there is a monopole in the configuration space of the Wess-Zumino model and show the relationship with the quantization of the monopole charge. We have found a Schwinger term in the commutator of left- and right-currents. This is an anomaly in a purely bosonic theory.     

Non-Abelian bosonization and topological aspects of BCS systems

It is shown that many features of the low energy behaviour of weak coupling BCS systems are topological in character. This is done by writing the BCS action as a Fermi surface sum of (1 + 1)-dimentional non-Abelian actions, each one of which can be bosonized à la Witten. This process leads to the correct current generating parts (as found by Cross) in the effective action for the gap function, and in addition a Wess-Zumino term. The mass and spin currents are calculated for the three-dimensional theory, and it is shown that upon averaging over all directions on the Fermi surface, the contribution from the Wess-Zumino term vanishes for a pure spin singlet or pure spin triplet gap, but not otherwise.     

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.     

Two-photon contributions to the Rosenbluth cross-section in the Skyrme model

We study two-photon contributions to the elastic electron-nucleon scattering within the Skyrme model. In particular we focus on the role of the anomaly that enters via the Wess-Zumino term and explain how this induces an axial current interaction.     

Chiral anomalies in supersymmetric theories

The supersymmetric non-abelian chiral anomaly is computed in a theory of chiral scalar superfields coupled to external gauge superfields, both in a vector-current conserving scheme and in a left-right symmetric scheme. The corresponding supersymmetric Wess-Zumino term is discussed; in particular we give an explicit expression for the anomalous bosonic term.     

Baryons as solitons and mass formulae

It is shown that the Wess-Zumino term gives the right quantum numbers for the baryons, which appear as solitons in current algebra lagrangians. In these models, the mass formulae for the baryons are derived.     

The WZ term of the spinning string and its on-shell structure

The Wess-Zumino term of the spinning string is constructed in terms of its anomalies using an extended field-antifield formalism. A new feature appears from the fact that the nonanomalous transformations do not form a subgroup. The algebra of the extended variables closes only using the equations of motion derived from the WZ term.     

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.     

BFT formalism and first order systems

The Abelian conversion of a class of constraints characteristic of first order systems is implemented in a general way. The corresponding Wess-Zumino terms are obtained. We illustrate the procedure with an example of charged matter coupled via a pure Chern-Simons term.