Abstract
This paper describes a general group theoretical analysis of the temperature–Hartree-Fock–Bogoliubov (HFB) equation and its solution. The action of the symmetry group G0 of the system on the HFB Hamiltonian, the HFB density matrix, and the HFB Green function are defined. It is shown that the HFB equation and its solution is classified by a subgroup G of G0, which is the invariance group of the HFB Hamiltonian, the HFB density matrix, and the HFB Green function corresponding the solution. General expression of the instability of a solution and its decomposition into R-rep (single-valued irreducible representation over the real number field) components of the invariance group of the solution are obtained. The self-consistent field (SCF) condition is decomposed into R-rep components of G0.
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