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Grassmann integral and Balian-Br\'ezin decomposition in Hartree-Fock-Bogoliubov matrix elements

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arxiv 1305.1682 v1 pith:MDJMSHQ5 submitted 2013-05-08 nucl-th

Takahiro Mizusaki , Makito Oi , Fang-Qi Chen , Yang Sun This is my paper
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keywords decompositionformulabalian-brbasiselementsezingrassmannhartree-fock-bogoliubov
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We present a new formula to calculate matrix elements of a general unitary operator with respect to Hartree-Fock-Bogoliubov states allowing multiple quasi-particle excitations. The Balian-Br\'ezin decomposition of the unitary operator (Il Nuovo Cimento B 64, 37 (1969)) is employed in the derivation. We found that this decomposition is extremely suitable for an application of Fermion coherent state and Grassmann integrals in the quasi-particle basis. The resultant formula is compactly expressed in terms of the Pfaffian, and shows the similar bipartite structure to the formula that we have previously derived in the bare-particles basis (Phys. Lett. B 707, 305 (2012)).

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