Toward a Microscopic Theory of Large Amplitude Collective Motions Based on the SO(2N+1) Lie Algebra of the Fermion Operators (「時間依存自己無撞着場の方法と量子化」研究会報告)

概要

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A microscopic theory of large amplitude collective motions is proposed which is based on the SO(2N+1) Lie algebra of the fermion operators. Following the idea of Kuriyama-Yamamura, a cononical condition for collective variables is imposed by adopting an SO(2N+1) wave function. Then we obtain eqations to determine a collective path on the SO(2N) group manifold and constraints governing the collective and "independent-particle" degrees of freedom. An approximate solution of our equation is shown to be the well-known RPA one in the small amplitude limit and approximate forms of the SO(2N+1) energy and density matrices are given. Our theory is strikingly contrast to the circumstances of the Kuriyama-Yamamura theory with the use of fermion coherent state representation which forces us to introduce inevitably anti-commuting Grassmann numbers.
素粒子論グループ素粒子研究編集部の論文
1984-03-20