Gauge Anomalies in Two Dimensions
In these lectures, I will try to explain how two-dimensional field theories in which gauge invariance is anomalously broken may be treated consistently and to outline the resultant interesting and unfamiliar features of such theories. As is well known, such anomalies are not special to two dimensions; they can occur in any number of dimensions where chiral fermions exist, and it was believed until a few years ago that in all such cases the gauge anomaly dealt a fatal blow to the theory. The anomaly was believed, variously, to lead to the failure of renormalizability, unitarity, Lorentz invariance, and even canonical consistency. This last was believed to fail because of the apparent conflict between the current-anomaly equation D VJ V = R(A μ ), where R(A μ ) is the anomalous divergence, and the gauge field equation D μF μV = J v , which implies D VJ V = 0.
KeywordsPoisson Bracket Gauge Invariance Gauge Field Lorentz Invariance Abelian Case
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