%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 }