Hamiltonian Formulation of the Theory with a Non-Abelian Chern–Simons Term Coupled to Fermions

Abstract

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) Poincaré 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 Poincaré 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