Abstract
Two-dimensional gauge models with chiral anomalies — "left-handed" QED and the chiral Schwinger model are consistently quantized in the frames of the minimal quantization method. The choice of the cone time as a physical time for the system of quantization is motivated. The well-known mass spectrum is found but with a fixed value of the regularization parameter a = 2. Such a unique solution is obtained due to the strong requirement of self-consistency of the minimal quantization method that is reflected in the physically motivated choice of the time axis.
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