Vector coherent state theory in new perspective: A hybrid mapping from fermion to fermion-boson space
Jin-Quan Chen, K. T. Hecht, Da Hsuan Feng · Physical Review C · 1991
Based on a hybrid mapping, the vector coherent state theory is revisited. The hybrid mapping of a fermion state with N coherent (collective) fermion pairs and u unpaired (noncollective) fermions leads to a hybrid state with N bosons and u fermions. The hybrid mapping is exact by which the formidable problem of finding the matrix elements of a fermion operator for a (2N+u)-fermion system is reduced to that for a u-fermion system. The Pauli effects are totally taken into account by the overlap matrix (the K matrix) for the fermion states. The application to a fermion system with the Sp(6)\ensuremath{\supset}U(3) dynamical symmetry is discussed where it is vividly seen that the occurrence of the dynamical Pauli factors is related to the fermion pair\ensuremath{\leftrightarrows}boson transformation. The intricate properties of the intrinsic operators and the K operator are discussed in detail.