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Anomalies and the quantum theory of chiral matter on a line

University of British Columbia

We give a brief review of anomalies in quantum field theory - where they arise, what they imply, and how they have been dealt with in the past. We suggest that theories with a gauge anomaly can be consistently quantized by applying the analogue of Dirac's formalism for classical constrained hamiltonian systems to the quantum theory. This suggestion is implemented for the archetypical chiral Schwinger model. By diagonalizing the hamiltonian, we show that the model is consistent, unitary, and Lorentz invariant. Its vector gauge boson aquires a gauge anomaly generated mass, and the fermionic sector bosonizes. We review the proposals for describing free chiral bosons and show that there are two which are not the same. The bosonization of a Dirac fermion in background gauge and gravitational fields is used to obtain the coupling of these two theories to backgrounds such that they are both the bosonization of a Weyl fermion in the same backgrounds. Nonabelian bosonization of gauged Dirac fermions in curved space has been used to obtain a chiral nonabelian Bose theory which corresponds to gauged Weyl fermions in curved space. This theory is the Siegel WZNW model coupled appropriately to background fields. We perform a canonical quantization of the Siegel WZNW theory using the BRST formalism. We find that by introducing an anomaly cancelling conformal field, it can be quantized for a large class of symmetry groups. For a certain subset of these groups the conformal field vanishes.

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2010-10-14

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http://hdl.handle.net/2429/29179

Physics

University of British Columbia

Graduate