Abstract
The family of all Hartree-Fock-Bogoliubov (HFB) states for a given set of r isosopin-spin orbitals form a set of coherent states. The set of antisymmetrized geminal power (AGP) states for a given set of r isospin-spin orbitals form a set of charge-projected coherent states, with the number of particles n as the “charge” and the HFB coherent state as the generating function. Both these coherent states are associated with the group SO(2 r). The approximate time evolution of the system generated by restricting the quantum mechanical evolution to the family of HFB and AGP coherent states is described as a classical dynamics with the energy of the coherent state as hamiltonian function. The phase space is isomorphic to the coset space SO(2 r)/U( r). The random phase approximation based on HFB and AGP states is derived by considering the harmonic approximation to the hamiltonian function. This work generalizes the group theoretical approaches to Hartree-Fock, and time-dependent Hartree-Fock theory by the use of non-number-conserving (HFB) and correlated (AGP) states.
Published Version
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