BRST Quantization of 2D-Yang Mills Theory with Anomalies

摘要

The BRST quantization of anomalous two dimensional (2D) Yang Mills (YM) theory isdiscussed. Since an oscillator basis for the YM Fock space is used, the anomaly appears already for a pure YM system and the constraints form a Kac-Moody algebra with negative central charge. The coupling of chiral fermions is discussed and it is found that the BRST cohomology for systems with chiral fermions in a sufficiently large representation of the gauge group is completely equivalent to the cohomology of the finite dimensional gauge group. For pure YM theory or YM theory coupled to chiral fermions in small representations there exists an infinite number of inequivalent cohomology classes. This is discussed in detail for the example of SU(2).