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-Brézin 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)).
%0 Generic
%1 Mizusaki2013Grassmann
%A Mizusaki, Takahiro
%A Oi, Makito
%A Chen, Fang-Qi
%A Sun, Yang
%D 2013
%K qft
%T Grassmann integral and Balian-Brézin decomposition in Hartree-Fock-Bogoliubov matrix elements
%U http://arxiv.org/abs/1305.1682
%X 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-Brézin 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)).
@misc{Mizusaki2013Grassmann,
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)).}},
added-at = {2019-02-23T22:09:48.000+0100},
archiveprefix = {arXiv},
author = {Mizusaki, Takahiro and Oi, Makito and Chen, Fang-Qi and Sun, Yang},
biburl = {https://www.bibsonomy.org/bibtex/22982295fd6e582fbb9f5ad1b6cf7d84e/cmcneile},
citeulike-article-id = {12334710},
citeulike-linkout-0 = {http://arxiv.org/abs/1305.1682},
citeulike-linkout-1 = {http://arxiv.org/pdf/1305.1682},
day = 8,
eprint = {1305.1682},
interhash = {1b3a6cd08092e510e6bf2faf6dd59759},
intrahash = {2982295fd6e582fbb9f5ad1b6cf7d84e},
keywords = {qft},
month = may,
posted-at = {2013-05-10 09:19:58},
priority = {2},
timestamp = {2019-02-23T22:15:27.000+0100},
title = {{Grassmann integral and Balian-Br\'ezin decomposition in Hartree-Fock-Bogoliubov matrix elements}},
url = {http://arxiv.org/abs/1305.1682},
year = 2013
}