Spectral properties on a circle with a singularity

T. Fülöp, Izumi Tsutsui, Taksu Cheon

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We investigate the spectral and symmetry properties of a quantum particle moving on a circle with a pointlike singularity (or point interaction). We find that, within the U(2) family of the quantum mechanically allowed distinct singularities, a U(1) equivalence (of duality-type) exists, and accordingly the space of distinct spectra is U(1) × [SU(2)/U(1)], topologically a filled torus. We explore the relationship of special subfamilies of the U(2) family to corresponding symmetries, and identify the singularities that admit an N = 2 supersymmetry. Subfamilies that are distinguished in the spectral properties or the WKB exactness are also pointed out. The spectral and symmetry properties are also studied in the context of the circle with two singularities, which provides a useful scheme to discuss the symmetry properties on a general basis.

Original languageEnglish
Pages (from-to)2737-2746
Number of pages10
JournalJournal of the Physical Society of Japan
Volume72
Issue number11
DOIs
Publication statusPublished - Nov 2003

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symmetry
supersymmetry
equivalence
interactions

Keywords

  • Circle
  • Point interaction
  • Point singularity
  • Quantum mechanics
  • Spectrum
  • Super-symmetry
  • Symmetries
  • WKB exactness

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Spectral properties on a circle with a singularity. / Fülöp, T.; Tsutsui, Izumi; Cheon, Taksu.

In: Journal of the Physical Society of Japan, Vol. 72, No. 11, 11.2003, p. 2737-2746.

Research output: Contribution to journalArticle

Fülöp, T. ; Tsutsui, Izumi ; Cheon, Taksu. / Spectral properties on a circle with a singularity. In: Journal of the Physical Society of Japan. 2003 ; Vol. 72, No. 11. pp. 2737-2746.
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