About the sign ambiguity in the evaluation of Grand Canonical traces for quasi-particle statistical density operators

Details About the sign ambiguity in the evaluation of Grand Canonical traces for quasi-particle statistical density operators About the sign ambiguity in the evaluation of Grand Canonical traces for quasi-particle statistical density operators

2009-09-02

arxiv.org/abs/0909.0333v2

Physics

Nuclear Physics

Nuclear Theory

15 pages with 2 figures

Scientific paper

A simple and general prescription for evaluating unambiguously the sign of the grand-canonical trace of quasi-particle statistical density operators (the so-called sign ambiguity in taking the square root of determinants) is given. Sign ambiguities of this kind appear in the evaluation of the grand-canonical partition function projected to good quantum numbers (angular momentum, parity and particle number) in the Hartree-Fock-Bogoliubov approximation at finite temperature, since traces are usually expressed as the square root of determinants. A comparison is made with the numerical continuity method.

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