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.
The explicit construction of an orthonormal basis for states of good spin, isospin and SU(4) Wigner supermultiplet symmetry is given in a Bargmann representation space. A complete set of quantum labels is provided by a Sp(3, !HI 3 U(3) complementary symmetry.
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