Representation theory and Wigner-Racah algebra of the SU(2) group in a noncanonical basis
نویسندگان
چکیده
The Lie algebra su(2) of the classical group SU(2) is built from two commuting quon algebras for which the deformation parameter is a common root of unity. This construction leads to (i) a not very well-known polar decomposition of the generators J− and J+ of the SU(2) group, with J+ = J † − = HUr where H is Hermitean and Ur unitary, and (ii) an alternative to the {J2, Jz} quantization scheme, viz., the {J2, Ur} quantization scheme. The representation theory of the SU(2) group can be developed in this nonstandard scheme. The key ideas for developing the Wigner-Racah algebra of the SU(2) group in the {J2, Ur} scheme are given. In particular, some properties of the coupling and recoupling coefficients as well as the Wigner-Eckart theorem in the {J2, Ur} scheme are examined in great detail. 1Dedicated to Professor Josef Paldus on the occasion of his 70th birthday. 1
منابع مشابه
An Alternative Basis for the Wigner-racah Algebra of the Group Su(2)
The Lie algebra of the classical group SU(2) is constructed from two quon algebras for which the deformation parameter is a common root of unity. This construction leads to (i) a (not very well-known) polar decomposition of the generators J − and J + of the SU(2) Lie algebra and to (ii) an alternative to the {J 2 , J 3 } quantization scheme, viz., the {J 2 , U r } quantization scheme. The key i...
متن کاملOn the Wigner-racah Algebra of the Group Su2 in a Non-standard Basis
The algebra su 2 is derived from two commuting quon algebras for which the parameter q is a root of unity. This leads to a polar decomposition of the shift operators J + and J − of the group SU 2 (with J + = J † − = HUr where H is Hermitean and Ur unitary). The Wigner-Racah algebra of SU 2 is developed in a new basis arising from the simultanenous diagonalization of the commuting operators J 2 ...
متن کاملTopics in Hidden Symmetries. Iv.
This note being devoted to some aspects of the inverse problem of representation theory explicates the links between researches on the Sklyanin algebras and the author’s (based on the noncommutative geometry) approach to the setting free of hidden symmetries in terms of ”the quantization of constants”. Namely, the Racah–Wigner algebra for the Sklyanin algebra is constructed. It may be considere...
متن کاملSU(N) Wigner-Racah algebra for the matrix of second moments of embedded Gaussian unitary ensemble of random matrices
Recently Pluhar and Weidenmüller [Ann. Phys. (N.Y.) 297, 344 (2002)] showed that the eigenvectors of the matrix of second moments of embedded Gaussian unitary ensemble of random matrices generated by k-body interactions (EGUE(k)) for m fermions in N single particle states are SU(N) Wigner coefficients and derived also an expression for the eigenvalues. Going beyond this work, we will show that ...
متن کاملSymmetry Adaptation and Wigner-Racah Algebras in Quantum Chemistry
The Wigner-Racah algebra of an arbitrary (finite or compact continuous) group is presented in an original way that constitutes a straightforward extension of the corresponding algebra of the rotation group. Illustrative examples are given around the rotation group and the octahedral group. The adaptation of the Wigner-Racah algebra of the double rotation group to one of its subgroups G is discu...
متن کامل