Hamiltonian Formulation of the Theory with a Non-Abelian Chern–Simons Term Coupled to Fermions
✍ Scribed by R. Banerjee; B. Chakraborty
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 535 KB
- Volume
- 247
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
A consistent field theoretical formulation of fermionic matter coupled to a non-abelian Chern Simons terms is usually regarded as problematic due to the violation of (classical) Poincare covariance. We discuss an alternative Hamiltonian formalism, developed by Faddeev Jackiw and Dirac, which overcomes this short-coming. We explicitly show that all the basic fields transform covariantly, so that the classical Poincare covariance is manifestly preserved. Schwinger conditions are verified. We also show that, within the abelian context, the conventional analysis of eliminating the gauge degrees of freedom in favour of the matter variables, is equivalent to the Dirac analysis. This is not true in the non-abelian case. A detailed analysis of the angular momentum reveals a group valued ``anomalous spin''. Some interesting consequences are derived.
1996 Academic Press, Inc.
I. Introduction
Recently there has been a spate of papers [1 10] discussing several aspects of dynamical systems with a Chern Simons (CS) three-form. It is important to note however, that these discussions have been mostly confined to abelian models. Since the non-abelian theory is interesting in its own right and perhaps simpler than the conventional one in four dimensions, its study deserves attention. The principal obstacle to this comes from the observation [11] that, in contrast to the abelian theory, the classical Poincare covariance of the nonabelian theory is lost. Thus a consistent formulation of the non-abelian CS theory has remained a long standing problem. Correspondingly any interesting consequences of this model have remained obscure.
In this paper an alternative method of Hamiltonian analysis, which is fundamentally different from the conventional analysis [11] of eliminating the gauge degrees of freedom in favour of the matter variables by using the classical equations of motion, will be discussed bypassing the above mentioned shortcoming. Within this method, we shall first consider the Faddeev Jackiw (FJ) [12] symplectic analysis. The energy-momentum (EM) tensor is defined using both the canonical (Noether) and symmetric structures. The role of constraints in establishing the compatibility between these different EM tensors is emphasized. All the basic fields are shown to transform covariantly under the various space-time generators. Classical Poincare article no.