Nuclear Physics B268 (1986) 413-426 0 North-Holland Publishing Company zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGF QUANTIZATION OF ANOMALOUS TWO-DIMENSIONAL MODELS LG. HALLIDAY, E. RABINOVICI* and A. SCHWIMMER** zyxwvutsrqponmlkjihgf Blackett Laboratory, Imperial College, Prince Consort Road, Lmdon SW 7 282 England M. CHANOWITZ Lawrence Berkeley Laboratory, Berkeley, California, USA Received 30 September 1985 Classes of anomalous two-dimensional theories are solved. In physical gauges the spectrum is not relativistic. Anomalous models in covariant gauges are equivalent to adding Wess-Zumino terms and going to a certain unitary gauge. The hamiltonian is generally not bounded from below. 1. Introduction The manifestation of the chiral anomaly in a hamiltonian formulation recently received a lot of attention [1,2]. In the A, = 0 gauge there is an anomalous contribution to the commutator of two Gauss’ law generators. As a consequence, Gauss’ law cannot be imposed as a constraint on the Hilbert space. Faddeev [3] made the interesting proposal that even without fully imposing Gauss’ law on the Hilbert space a physically sensible theory may emerge. Since in a physical (A, = 0) gauge the Hilbert space contains only positive norm states the potential problem may be the lack of Lorentz invariance. The solution to this problem suggested in ref. [3] was a possible equivalence between the theory in the A, = 0 gauge and a Lorentz covariant theory in which the anomaly is cancelled by adding a Wess-Zumino [4] term. In this paper we examine the above proposal in classes of solvable two-dimen- sional models. We will follow, as close as possible, the way in which the general arguments work in our models. In sect. 2 we solve a class of chiral models in the A, = 0 gauge. We obtain the full spectrum and we discuss the conditions under which the spectrum is relativistic. In sect. 3 we consider a parity conserving model and compare its spectrum with chiral models. * On leave from the Racah Institute for Physics, Hebrew University, Jerusalem, Israel. ** On leave from the Weizmann Institute, Rehovot, Israel. 413