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On the degeneracy in the ground state of the N=2 Wess–Zumino supersymmetric quantum mechanics
| Title: | On the degeneracy in the ground state of the N=2 Wess–Zumino supersymmetric quantum mechanics |
| Authors: | Arai, Asao Browse this author →KAKEN DB |
| Keywords: | supersymmetry | | quantum mechanics | | degeneration | | ground states | | polynomials | | potentials | | eigenfunctions | | coupling constants | | symmetry breaking | | hilbert space |
| Issue Date: | Dec-1989 |
| Publisher: | American Institute of Physics |
| Journal Title: | Journal of Mathematical Physics |
| Volume: | 30 |
| Issue: | 12 |
| Start Page: | 2973 |
| End Page: | 2977 |
| Publisher DOI: | 10.1063/1.528485 |
| Abstract: | 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: | http://www.aip.org/ |
| Type: | article |
| URI: | http://hdl.handle.net/2115/13683 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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