Symmetry, Duality, and Anholonomy of Point Interactions in One Dimension
✍ Scribed by Taksu Cheon; Tamás Fülöp; Izumi Tsutsui
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 212 KB
- Volume
- 294
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
We analyze the spectral structure of a one-dimensional quantum mechanical system with point interaction, which is known to be parametrized by the group U (2). Based on the classification of the interactions in terms of symmetries, we show, on a general basis, how the fermion-boson duality and the spectral anholonomy recently discovered can arise. A vital role is played by a hidden su(2) formed by a certain set of discrete transformations, which becomes a symmetry if the point interaction belongs to a distinguished U (1) subfamily in which all states are doubly degenerate. Within the U (1), there is a particular interaction that admits the interpretation of the system as a supersymmetric Witten model.