Hartree-Fock-Bogoliubov theory without quasiparticle vacua

Hartree-Fock-Bogoliubov (HFB) theory is generalized by eliminating the restriction to quasiparticle vacuum states. However, the fundamental HFB transformation to quasiparticles is retained. The theory is formulated in terms of the quasiparticle density matrix $R$, but, in contrast to conventional HFB, there is no restriction to vacuum densities $R^2=R$.