The Bloch-Messiah theorem and its application to overlaps

Abstract: The Bogoliubov transformation is the starting point for the Hartree-Fock-Bogoliubov method and thus for many theoretical approaches that describe heavy nuclei. This transformation is based on two matrices, denoted by U and V, which are called Bogoliubov amplitudes. In this paper the properties of these matrices are investigated. Bogoliubov amplitudes are generated using BCS wavefunctions. The Bloch-Messiah theorem and the resulting Bloch-Messiah decomposition are discussed as well as a newfound restriction on the transformation matrix D from the BM decomposition. Different formulas are presented to compute the overlap between the generated wavefunctions.