A Schwinger term in q-deformed su(2) algebra

Abstract

An extra term generally appears in the q-deformed su(2) algebra for the deformation parameter q = exp 2πiθ, if one combines the Biedenharn-Macfarlane construction of q-deformed su(2), which is a generalization of Schwinger's construction of conventional su(2), with the representation of the q-deformed oscillator algebra which is manifestly free of negative norm. This extra term introduced by the requirement of positive norm is analogous to the Schwinger term in current algebra. Implications of this extra term on the Bloch electron problem analyzed by Wiegmann and Zabrodin are briefly discussed.