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Progress of Theoretical Physics

An a priori Quantized Time-Dependent Hartree-Bogoliubov Theory: A Generalization of the Schwinger Representation of Quasi-Spin to the Fermion-Pair Algebra

Masao Yamamura, Seiya Nishiyama

Published Jul 1, 1976• 22 citations
Publisher
DOI
10.1143/ptp.56.124

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The generalized Schwinger representation of the fermion pairs is reformulated with the aim of investigating the applicability to the anharmonicity. Through this reformulation, the seniority quantum number and quasi-boson operator as the generator of higher seniority states are introduced into the Schwinger boson space. An approximate diagonalization of pairing Hamiltonian gives the same result as that of the BCS-Bogoliubov theory.

Progress of Theoretical Physics•May 1, 1978•1 citation
An induced representation of an SO(2N + 1) group has been obtained from a group extension of the SO(2N) Bogoliubov transformation for fermions to a new canonical transformation group. Embedding the SO(2N + 1) group into an SO(2N + 2) group and using the SO(2N + 2)/U(N + 1) coset variables, we develop an extended time dependent Hartree–Bogoliubov (TDHB) theory in which paired and unpaired modes are treated in an equal manner. The extended TDHB theory applicable to both even and odd fermion systems is a time dependent self-consistent field (TDSCF) theory with the same level of the mean field approximation as the usual TDHB theory for even fermion systems. We start from the Hamiltonian of the fermion system which includes, however, the Lagrange multiplier terms to select the physical spinor subspace. The extended TDHB equation is derived from the classical Euler–Lagrange equation of motion for the SO(2N + 2)/U(N + 1) coset variables in the TDSCF. The final form of the extended TDHB equation can be expressed through the variables as the representatives of the paired mode and the unpaired mode. We introduce the quasi anti-commutation relation approximation for the fermion. The parameters included in the Lagrangian multiplier terms are determined under the quasi anti-commutation relation approximation.