Abstract
It is shown that the set of Antisymmetrized Geminal Power (AGP) states for a given set of r spin orbitals form a set of charge-projected coherent states, with the number of particles n acting as the “charge”. The family of Hartree-Fock-Bogoliubov (HFB) states for the same set of spin orbitals form a set of coherent states that are generating functions for the AGP coherent states for all n. The approximate time evolution of the system generated by the quantum mechanical hamiltonian restricted to such states is described as a classical dynamics on a generalized phase space. The phase space is isomorphic to the coset space SO(2r)/U(r). Ramifications of this for the energy optimization of AGP states and HFB states are discussed. The Random Phase Approximation based on such states is derived by considering small amplitude oscillations in this phase space. This work generalizes the group theoretical approaches to Hartree-Fock and time dependent Hartree-Fock to correlated and non-number conserving states.
Published Version
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