English

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

Nuclear Theory 2013-07-30 v1

Abstract

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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Cite

@article{arxiv.1305.1682,
  title  = {Grassmann integral and Balian-Br\'ezin decomposition in Hartree-Fock-Bogoliubov matrix elements},
  author = {Takahiro Mizusaki and Makito Oi and Fang-Qi Chen and Yang Sun},
  journal= {arXiv preprint arXiv:1305.1682},
  year   = {2013}
}

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5 pages