Gauge invariance in second quantization: Applications to Hartree-Fock and generalized random-phase approximations

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Abstract
Gauge transformations on the wave function are formulated in second quantization, and it is shown that the Schrödinger equation in second quantization is form invariant under local gauge transformations. Hartree-Fock theory is examined in the second-quantization formalism and shown to be gauge invariant in spite of being nonlocal, contrary to recent reports. Rowe's equation-of-motion method, of which the random-phase approximation is a special case, is also shown to be gauge invariant. The length and velocity forms of the dipole oscillatory strengths are shown to be equal in Rowe's theory under certain conditions, which the random-phase approximation satisfies.