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The standard Bogoliubov transformation is generalized to enable fermionnumber parity breaking. The new transformation can diagonalize fermionHamiltonians that are quadratic in fermion and number parity operators. Thisnew variational freedom cannot lower the energy of Hamiltonians that conservenumber parity. However, it has value as a minimal mechanism for continuouslyvarying between states of different fermion number, regardless of numberparity.

Generalized unitary Bogoliubov transformation that breaks fermion number parity