Nonexistence of the continuum ferromagnet

by D. A. Dubin and R. F. Streater; Il Nuovo Cimento, 50, 154-157, 1967.

ABSTRACT

By considering the representation of SU(2) of spin 1/2, and a cyclic vector of the representation at each point of a continuous space, we obtain a scalar product for the continuous product that is not positive semi-definite. This shows that the continuous tensor product of group representations does not exist in general. A similar example appears in ``Sur les produits tensorial continues d'espace hilbertiens, by A. Guichardet and A. Wulfsohn, J. Functl. Anal., 2, 371-377, 1968.

This problem has a complete solution in a later paper.