Representations of U(1,q) and Constructive Quaternion Tensor Products
Abstract
Description
The representation theory of the group U(1,q) is discussed in detail because of its possible application in a quaternion version of the Salam-Weinberg theory.
As a consequence, from purely group theoretical arguments we demonstrate that the eigenvalues must be right-eigenvalues and that the only consistent scalar products are the complex ones. We also define an explicit quaternion tensor product which leads to a set of additional group representations for integer ``spin''.
28 pages, Latex, Dipartimento di Fisica, Universita di Lecce INFN-Sezione di Lecce
28 pages, Latex, Dipartimento di Fisica, Universita di Lecce INFN-Sezione di Lecce