Anomalous Gauge Theories Research Articles

ANOMALOUS GAUSS LAW ALGEBRAS

Supplementing the Gauss law operator of an anomalous gauge theory with a certain set of functionals of the gauge potentials, one obtains a closed algebra. The algebras obtained in this way are Abelian extensions of the Lie algebra of the group of gauge transformations, and are natural generalizations of Kac-Moody algebras, both in two and four dimensions.

CONSTRAINED HAMILTONIAN STRUCTURE OF THE CHIRALLY GAUGED WESS-ZUMINO-WITTEN MODEL

We construct the canonical formulation of the left-gauged non-Abelian Wess-Zumino-Witten (WZW) model in four dimensions using Dirac's method of constraints. This study is motivated by our interest in establishing the canonical consistency of anomalous non-Abelian gauge theories of chiral fermions, which are believed to be approximated by the corresponding WZW action in the low energy limit. We introduce in the action a free parameter α, reflecting some of the regularization ambiguities of the anomaly. We find that for α > 1, the WZW model is classically consistent and has a unique positive Hamiltonian, suggesting that the corresponding anomalous fermionic theory will also be consistent and unitary. The case α = 1 is also studied and is shown to have some remarkable properties. Finally, some implications of our results for the Faddeev-Shatashvili model are pointed out.

ISOMORPHIC REPRESENTATIONS OF ANOMALOUS CHIRAL GAUGE THEORIES

Anomalous chiral gauge theories allow for gauge invariant and gauge noninvariant descriptions. We show that these are isomorphic and use this result to comment on misinterpretations of some aspects of the chiral Schwinger model. We also use this model to demonstrate how the isomorphism emerges within the Hamiltonian formalism.

Comment on "Noncommutative electric fields and consistency in anomalous gauge theories"

A Comment on the Letter by R. Banerjee, Phys. Rev. Lett. 61. 514 (1988).Received 24 August 1988DOI:https://doi.org/10.1103/PhysRevLett.63.336©1989 American Physical Society

Perturbative method for extracting the algebra of constraints in an anomalous chiral gauge theory.

Following a recent suggestion, we consider a possible method for extracting in perturbation theory the algebra of the constraints in anomalous chiral gauge theories by studying the correlation function of a modified theory containing an explicit gauge symmetry-breaking term. We illustrate the method for a two-dimensional chiral model, where exact operator solutions can be obtained.

Gauge-invariant reformulation of an anomalous gauge theory

An anomalous gauge theory can be reformulated in a gauge invariant way without any change in its physical content. This is demonstrated here for the exactly soluble chiral Schwinger model. Our gauge invariant version is very different from the Faddeev-Shatashvili proposal [L.D. Faddeev and S.L. Shatashvili, Theor. Math. Phys. 60 (1984) 206] and involves no additional gauge-group-valued fields. The status of the “gauge” A 0=0 sometimes used in anomalous theories is also discussed and justified in our reformulation.

Quantization of anomalous gauge theories on a lattice

We discuss advantages and disadvantages of three equivalent lattice actions proposed before for anomalous chiral gauge theories. Applications to the chiral Scwinger model and the 4 dimensional chiral QED are presented.

Anomalous gauge theories as constrained Hamiltonian systems

Anomalous gauge theories considered as constrained systems are investigated. The effects of chiral anomaly on the canonical structure are examined first for nonlinear σ-model and later for fermionic theory. The breakdown of the Gauss law constraints and the anomalous commutators among them are studied in a systematic way. An intrinsic mass term for gauge fields makes it possible to solve the Gauss law relations as second class constraints. Dirac brackets between the time components of gauge fields are shown to involve anomalous terms. Based upon the Ward-Takahashi identities for gauge symmetry, we investigate anomalous fermionic theory within the framework of path integral approach.

Role of the noncanonical transformation in anomalous gauge theories.

The method for calculating the commutator anomalies in anomalous Abeliangauge theories proposed by Yeung and Yu is reanalyzed based on the theory ofthe noncanonical transformation. Their method is easily extended to thenon-Abelian theory, but in general it does not lead to the correct Schwingerterm.

THE GAUSS OPERATOR IN ANOMALOUS GAUGE THEORIES: A HAMILTONIAN FORMULATION

The time dependence of the Gauss law operator in anomalous gauge theories has been investigated in the Hamiltonian formulation using the point-splitting regularization. Consistent results have been obtained in both 1+1 and 1+3 dimensions.

Derivation of anomalous commutator and Jacobian from very general conditions.

Using only the equation of motion and the canonical commutator of anomalous gauge theories, we show clearly the relation between the Schwinger-Jackiw-Johnson (SJJ) term, the anomalous Jacobian, and the current-divergence anomaly by obtaining both the SJJ term and the anomalous Jacobian from the current-divergence anomaly.

Some algebraic identities in anomalous gauge theories

Some useful algebraic relations between the anomaly of Dmu Jmu and anomalous commutators are derived using only the canonical commutators and the equation of motion. Their applications are discussed.

A SIMPLE MANNER FOR THE QUANTIZATION OF ANOMALOUS GAUGE THEORIES

The chiral Schwinger model is a massive vector theory at the quantum level. We construct the gauge invariant action using Stueckelberg formalism from this. Then the resulting action is exactly the same as the modified action obtained by path-integral formalism. We propose a simple manner for the quantization of anomalous gauge theories.

Noncanonical features in an anomalous gauge theory

Noncanonical features in an anomalous gauge theory

CONSTRUCTION OF HILBERT SPACE IN THE ANOMALOUS GAUGE THEORY

We analyze the abelian and non-abelian anomalous gauge theory through the BRS approach. We construct the positive norm Hilbert space and obtain the physical fields in the abelian case. By the same method, we construct the physical subspace in the non-abelian case for a=2. Finally, we discuss the physical observables and other related problems.

A ?-function method for weyl fermionic determinants

We present an extension of the ζ-function method adapted to handle the regularization of Dirac operator determinants when Weyl fermions are present. The method we propose makes use of an auxiliary operator which takes into account regularization ambiguities in anomalous gauge theories. As an application, we consider a two-dimensional model where these ambiguities allow for the definition of a consistent quantum theory.

CHIRALLY GAUGED WESS-ZUMINO-WITTEN MODEL AS A CONSTRAINED SYSTEM

With the intention of finding a consistent Hamiltonian description of the anomalous nonabelian gauge theories in four dimensions, we examine algebraic properties of the Gauss-law constraints for the chirally gauged nonlinear σ-model with a Wess-Zumino-Witten term. A relation which, in the Weyl gauge, reduces to Fujikawa’s relation ∂0Ga(x) =i(DµJμ)a (x), is verified. Finally we attempt to quantize the system at the tree level by explicitly calculating the Dirac brackets.

Algebraic Consistency in Anomalous Gauge Theories

Algebraic Consistency in Anomalous Gauge Theories

BRS analysis of the non-Abelian chiral Schwinger model.

We analyze the non-Abelian anomalous gauge theory with the Wess-Zumino action for a>1, where a is a bosonization ambiguity, through the Becchi-Rouet-Stora (BRS) approach. We construct the positive-definite-norm Hilbert space. Further unitarity of the total S matrix is checked. From the Hamiltonian formulation, we study the time evolution of the BRS charge.

Noncommutative electric fields and consistency in anomalous gauge theories.

It is shown that noncommutative electric fields (E) are essential to preserve algebraic consistency in anomalous gauge theories. A consistency condition is used to reveal different structures for the E-E commutator.