Theq-number Schwinger Term and the Breakdown of the Associative Law for Current Operators
Gaku Konisi, Kunio Yamamoto · Progress of Theoretical Physics · 1967
It is suggested that there cannot exist the q-number Schwinger term which was discussed by Buccella, Veneziano, Gatto and Okubo in order to explain incompatibility of the usual commutation relations of current operators with the Jacobi identity. The incompatibility arises from the fact that current operators do not satisfy the associative law of multiplication. This is because they are not the ordinary linear operators but distribution-valued operators on the Hilbert space.