BRAID GROUP-RELATED ALGEBRAS, THEIR REPRESENTATIONS AND GENERALIZED HYDROGENLIKE SPECTRA

ARIK M., AYDIN F., HIZEL E., KORNFILT J., YILDIZ A.

JOURNAL OF MATHEMATICAL PHYSICS, vol.35, no.6, pp.3074-3088, 1994 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 35 Issue: 6
  • Publication Date: 1994
  • Doi Number: 10.1063/1.530506
  • Journal Name: JOURNAL OF MATHEMATICAL PHYSICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3074-3088
  • Yıldız Technical University Affiliated: Yes

Abstract

Representations of the n-braid group where generators are given by matrices whose elements belong to a noncommutative algebra are discussed. Representation of this algebra in a Hilbert space generalizes the Burau representation. Two algebras which are closely related and are physically indistinguishable provided that a particular eigenvalue is fine tuned are discussed. It is shown that the generalized oscillator system given by one of the algebras generates a hydrogenlike spectrum.