The unitary group formulation of the many-body problem: an alternative to second quantization

F.A. Matsen

F. A. Matsen, Constance J. Nelin

F. A. Matsen

Abstract The fermion unitary group formulation (UGF) of many‐body theory is based on the unitary group U(2n) where n is the number of freeon orbitals. This formulation, which conserves particle‐number but not spin, is isomorphic to the particle‐number‐conserving, second‐quantized formulation (SQF). In UGF we derive the familiar diagrammatic algorithm for matrix elements, M(Y) = (−1)H+L where H and L denote the numbers of hole lines and loops in the diagram D(Y) of M(Y). The unitary group derivation is considerably simpler than is the conventional, second‐quantized derivation that employs time‐dependence, Wick's theorem, normal‐order, and contractions. In neither fermion UGF nor SQF is spin conserved. We carry out in UGF the spin‐projection (symmetry adaptation to SU(2)) of the fermion vectors and obtain with a spin‐free Hamiltonian the same matrix elements as with the freeon UGF (part 24 of this series). The fermion unitary group formulation for a spin‐free Hamiltonian should be regarded as an alternate path to spin‐free quantum chemistry.

F. A. Matsen

Abstract We present the freeon, singlet, unitary group formulation of many‐body theory as an alternative to the particle‐number‐conserving, spin‐projected, fermion, second‐quantized formulation. It is based on the generator‐state‐approach (GSA) developed in part 23 of this series. We develop C1, perturbation, coupled‐cluster, and random‐phase theories.

Kenji Suzuki, Ryoji Okamoto