Vector coherent state theory and its application to the orthogonal groups

Abstract

Vector coherent state theory is developed and presented in a form that explicitly exhibits its general applicability to the ladder representations of all semisimple Lie groups and their Lie algebras. It is shown that, in a suitable basis, the vector coherent state inner product can be inferred algebraically, by K-matrix theory, and changed to a simpler Bargmann inner product thereby facilitating the explicit calculation of the matrix representaions of Lie algebras. Applications are made to the even and odd orthogonal Lie algebras.