On the SO(2N+1) Regular Representation of Operators and Wave Functions of Fermion Many-Body Systems

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概要

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• Properties and implications of the SO(2N+1) regular representation of a fermion system, which is a representation on the SO(2N+1) group proposed recently by us, are studied. By using the independent variables of the SO(2N+1) group, a representation of fermion annihilation-creation and pair operators is obtained which is an extension of the Dyson representation to cover both paired and unpaired modes. The structures of SO(2N+1) spinor space and the SO(2N+1) wave function are determined. An integral and a differential Schrodinger equation on the SO(2N+1) spinor space are derived which are applicable to both even and odd fermion systems. The structures of the symmetry projected SO(2N+1) wave function and Schrodinger operator are determined. It is shown that odd fermion systems can be treated with an analogous way as even fermion systems by using a special SO(2N+1) canonical transformation which is very similar to the Bogoliubov transformation but corresponds to an improper rotation in the O(2N) group.

• 理論物理学刊行会の論文
• 1977-12-25

著者

• Fukutome Hideo

  Department Of Physics Faculty Of Science Kyoto University

• FUKUTOME Hideo

  Department of Physics, Faculty of Science, Kyoto University

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