Symmetry restoration in hartree-fock-bogoliubov based theories

We present a Pfaffian formula for projection and symmetry restoration for wave functions of the general Bogoliubov form, including quasiparticle excited states and linear combinations of them. This solves a long-standing problem in calculating states of good symmetry, arising from the sign ambiguity of the commonly used determinant formula. A simple example is given of projecting a good particle number and angular momentum from a Bogoliubov wave function in the Fock space of a single j-shellThis work was supported in part by the U.S. Department of Energy under Grant No. DE-FG02- 00ER41132, and by the National Science Foundation under Grant No. PHY-0835543. The work of L. M. R. was supported by MICINN (Spain) under Grants No. FPA2009-08958, and No. FIS2009-07277, as well as by Consolider-Ingenio 2010 Programs CPAN Grant No. CSD2007-00042 and MULTIDARK Grant No. CSD2009-0006