Associativity in Wess-Zumino model and Kac-Moody algebra

Abstract

Topological quantization of the coefficient of the Wess-Zumino model is investigated in Hamilton formalism. Quantization is shown to be required from the associativity of the operators. Center of the Kac-Moody algebra is also quantized from the requirement of the associativity. We show that there is a monopole in the configuration space of the Wess-Zumino model and show the relationship with the quantization of the monopole charge. We have found a Schwinger term in the commutator of left- and right-currents. This is an anomaly in a purely bosonic theory.