SU(2){sub q} in a Hilbert space of analytic functions
- Instituto Pedagogico de Caracas (Venezuela)
The algebra SU(2){sub q} is realized in a Hilbert space H{sub q}{sup 2} of analytic functions; the starting point is the differential realization of operators that satisfy q-algebra in a Hilbert space H{sub q}. The Weyl realization of SU(2){sub q} is constructed exhibiting the reproducing kernel and the principal vectors; the noncommutativity of the matrix elements of a 2x2 linear representation of SU(2){sub q} is obtained as consistency conditions for coupling j1=j2=1/2 to j=0,1; the derivation of Clebsch-Gordan coefficients is sketched and the q-generalization of the rotation matrices is included. The unitary correspondence of H{sub q} with a Hilbert space of complex functions of a real variable is also studied. The study presented in this paper follows Bargmann`s formalism for the rotation group as closely as possible. 20 refs.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 133257
- Journal Information:
- International Journal of Theoretical Physics, Vol. 31, Issue 6; Other Information: PBD: Jun 1992
- Country of Publication:
- United States
- Language:
- English
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