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On the degeneracy in the ground state of the N=2 Wess–Zumino supersymmetric quantum mechanics

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タイトル: On the degeneracy in the ground state of the N=2 Wess–Zumino supersymmetric quantum mechanics
著者: Arai, Asao 著作を一覧する
キーワード: supersymmetry
quantum mechanics
degeneration
ground states
polynomials
potentials
eigenfunctions
coupling constants
symmetry breaking
hilbert space
発行日: 1989年12月
出版者: American Institute of Physics
誌名: Journal of Mathematical Physics
巻: 30
号: 12
開始ページ: 2973
終了ページ: 2977
出版社 DOI: 10.1063/1.528485
抄録: It is known that the N=2 Wess–Zumino supersymmetric quantum mechanical model has p–1 degenerate zero-energy ground states consisting of only bosonic states, where p>3 is the degree of the polynomial superpotential V(z)(z∈C) of the model [Jaffe et al. Ann. Phys. (NY) 178, 313 (1987)]. In this paper, the mathematical structure of the degenerate ground states is analyzed in the special case V(z)=λz^p (λ>0). The following facts are discovered: (i) there exists a strongly continuous one parameter unitary group acting as a symmetry group in the quantum system under consideration; (ii) the generator of the symmetry group has infinitely many eigenspaces Hm, m∈Z, and the bosonic part H+ of the Hamiltonian of the model is reduced by each of them; and (iii) there exist exactly p–1 Hm's in each of which the reduced part of H+ has a unique zero-energy ground state. It is noted also that H+ has infinitely many generalized eigenfunctions with eigenvalue zero. Moreover, a family of operators interrelating the zero-energy ground states is constructed. The coupling constant dependence of the nonzero eigenvalues of H+ is exactly found.
Rights: Copyright © 1989 American Institute of Physics
Relation (URI): http://www.aip.org/
資料タイプ: article
URI: http://hdl.handle.net/2115/13683
出現コレクション:雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

提供者: 新井 朝雄

 

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