Canonical commutation relations, the Weierstrass Zeta function, and infinite dimensional Hilbert space representations of the quantum group Uq(s-fraktur signl-fraktur sign2)

Journal of Mathematical Physics

Volumn 37, Issue 9, 1996, Pages 4203-4218

  Arai, Asao ^a  

^a HOKKAIDO UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0038973494     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.531797     Document Type: Article

References (14)

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2. C. R. Putnam, Commutation Properties of Hilbert Space Operators (Springer-Verlag, Berlin, 1967).
3. Y. Aharonov and D. Bohrn, "Significance of electromagnetic potentials in the quantum theory," Phys. Rev. 115, 485-491 (1959).
4. H. Kurose and H. Nakazato, "Geometric construction of *-representation of the Weyl algebra with degree 2," preprint, 1994.
5. A. Arai, "Properties of the Dirac-Weyl operator with a strongly singular gauge potential," J. Math. Phys. 34, 915-935 (1993).
6. A. Arai, "Gauge theory on a non-simply conneted domain and representations of canonical commutation relations," J. Math. Phys. 36, 2569-2580 (1995).
7. A. Arai, "Representation of canonical commutation relations in a gauge theory, the Aharanov-Bohm effect, and the Dirac-Weyl operator," J. Nonlin. Math. Phys. 2, 247-262 (1995).
8. P. B. Wiegmann and A. V. Zabrodin, "Quantum groups and magnetic translations Bethe ansatz for Asbel-Hofstadter problem," Nucl. Phys. B 422, 495-514 (1994).
9. See Remark 2.3 in Ref. 5.
10. M. Reed and B. Simon, Methods of Modern Mathematical Physics (Academic, New York, 1972), Vol. I.
11. C. Kassel, Quantum Groups (Springer-Verlag, New York, 1995).
12. In this paper, an algebra means an algebra over the complex field C.
13. See, e.g., Chap. VI, Definition VI.1.1 in Ref. 11.
14. O. Bratteli and D. W. Robinson, Operator Algebra and Quantum Statistical Mechanics 1 (Springer-Verlag, New York, 1979).