Generator coordinate method approach to the dynamic group representation

Abstract

The generator coordinate method approach to the dynamic group representation is discussed in general. In various cases, either in group space or in coset space, representations of the dynamic group can readily be obtained with the generator coordinate method. Boson representation is just one form of the generator coordinate method approach to the dynamic group representation. Various representations of the dynamic group are described by the generator coordinate method approach to the dynamic group representation in a unified way. Not only is the algebraic structure of generators preserved, but also conditions imposed by (a) the Pauli principle, (b) symmetry properties, (c) dynamic properties, and (d) other concrete properties of nuclear systems are well incorporated in these representations, so that the original fermion representation is faithfully realized. The generator coordinate method approach to the dynamic group representation is strictly a transformation theory from the fermion representation to continuous variable or boson representations of the dynamic group. Examples are given for showing the essence and the prospects of applications of the generator coordinate method approach to the dynamic group representation.