SU(2)
q
in a Hilbert space of analytic functions |
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Authors: | Simón Codriansky |
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Institution: | (1) Centro de Física, IVIC, 1020-A Caracas, Venezuela;(2) Departamento de Matemáticas y Física, Instituto Pedagógico de Caracas, 1010 Caracas, Venezuela |
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Abstract: | The algebraSU(2)
q
is realized in a Hilbert spaceH
q
2
of analytic functions; the starting point is the differential realization of operators that satisfyq-algebra in a Hilbert spaceH
q. The Weyl realization ofSU(2)
q
is constructed exhibiting the reproducing kernel and the principal vectors; the noncommutativity of the matrix elements of a 2×2 linear representation ofSU(2)
q
is obtained as consistency conditions for couplingj1=j2=1/2 toj=0, 1; the derivation of Clebsch-Gordan coefficients is sketched and theq-generalization of the rotation matrices is included. The unitary correspondence ofH
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. |
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Keywords: | |
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