R. Rajaraman

Hamiltonian formulation of the anomalous chiral Schwinger model

We construct the hamiltonian formulation of the anomalous chiral Schwinger model, which has recently been shown to yield a consistent unitary theory. The impact of the anomaly on the constraints of the system is exhibited and the system is quantized using an appropriate hamiltonian consistent with the constraints.

New results on systems with second-class constraints

We show how, for large classes of systems with purely second-class constraints, further information can be obtained about the constraint algebra. In particular, a subset consisting of half the full set of constraints is shown to have vanishing mutual brackets. Some other constraint brackets are also shown to be zero. The class of systems for which our results hold includes examples from non-relativistic particle mechanics as well as relativistic field theory. The results are derived at the classical level for Poisson brackets, but in the absence of commutator anomalies the same results will hold for the commutators of the constraint operators in the corresponding quantised theories.

Gauge-invariant reformulation of an anomalous gauge theory

Abstract 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.

Anomalous non-abelian gauge theory in two dimensions

We consider the two-dimensional model of a U(N) gauge field coupled to just the right-handed current of N massless fermions. We show, using its bosonized version, that this model, although anomalous and non-gauge invariant, formally yields a consistent unitary Lorentz-invariant quantum theory. As by-products, the commutators of the currents and to the Gauss-law generators are obtained explicitly.

On solitons with half integral charge

Can certain soliton states, with half integral expectation value of charge, be also eigenstates of charge X with half integral eigenvalue? It can be so only with a somewhat sophisticated definition of charge.

Gauge-invariant reformulation of theories with second-class constraints

Given a classical dynamical theory with second-class constraints, it is sometimes possible to construct another theory with first-class constraints, i.e., a gauge-invariant one, which is physically equivalent to the first theory. We identify some conditions under which this may be done, explaining the general principles and working out several examples. Field theoretic applications include the chiral Schwinger model and the non-linear sigma model. An interesting connection with the work of Faddeev and Shatashvili is pointed out.

On anomalous U(1) gauge theory in four dimensions

We discuss the consistency, unitarity and Lorentz invariance of an anomalous U(1) gauge theory in four dimensions. Our analysis is based on an effective low-energy action valid in the chiral symmetry broken phase. The allegedly bad properties of anomalous theories (except non-renormalizability) are examined. It is shown that, in the low-energy context, the theory can be consistently and unitarily quantised, and is formally Lorentz covariant.

Degrees of freedom and the quantization of anomalous gauge theories

Abstract We show, for the two-dimensional case, that the anomalous gauge theory of chiral fermions yields degrees of freedom whose number depends on the regularization procedure. For a particular regularization, the gauge fields have dim [ rG ]-rank[ rG ] surviving degrees of freedom, while for others this number changes to 2 dim [ rG ] . Our procedure and results are compared with Faddeevs recent suggestions on how to quantize anomalous gauge theories. We conclude with some remarks on the four-dimensional case.

A FIELD THEORY FOR THE READ OPERATOR

We introduce a new field theory for studying quantum Hall systems. The quantum field is a modified version of the bosonic operator introduced by Read. In contrast to Reads original work we do not work in the lowest Landau level alone, and this leads to a much simpler formalism. We identify an appropriate canonical conjugate field, and write a Hamiltonian that governs the exact dynamics of our bosonic field operators. We describe a Lagrangian formalism, derive the equations of motion for the fields and present a family of mean-field solutions. Finally, we show that these mean field solutions are precisely the Laughlin states. We do not, in this work, address the treatment of fluctuations.

CPN solitons in quantum Hall systems

Abstract:We present here an elementary pedagogical introduction to CPN solitons in quantum Hall systems. We begin with a brief introduction to both CPN models and to quantum Hall (QH) physics. We then focus on spin and layer-spin degrees of freedom in QH systems and point out that these are in fact CPN fields for N = 1 and N = 3. Excitations in these degrees of freedom will be shown to be topologically non-trivial soliton solutions of the corresponding CPN field equations. We conclude with a brief summary of our own recent work in this area, done with Sankalpa Ghosh.