316 research outputs found
Quantizations of D=3 Lorentz symmetry
Using the isomorphism
we develop a new
simple algebraic technique for complete classification of quantum deformations
(the classical -matrices) for real forms and
of the complex Lie algebra in
terms of real forms of : ,
and . We prove that the
Lorentz symmetry
has three different Hopf-algebraic quantum deformations which are expressed in
the simplest way by two standard and
-analogs and by simple Jordanian
twist deformations. These quantizations are
presented in terms of the quantum Cartan-Weyl generators for the quantized
algebras and as well as in
terms of quantum Cartesian generators for the quantized algebra
. Finaly, some applications of the deformed Lorentz
symmetry are mentioned.Comment: 22 pages, V2: First and final sections (Sect. 1, Sect. 6) has been
partialy rewritten and extended, in Sect. 2-4 only minor corrections, in
Sect. 5 notational changes and the clarifications of some formulas; 13 new
references adde
On a general analytical formula for U_q(su(3))-Clebsch-Gordan coefficients
We present the projection operator method in combination with the
Wigner-Racah calculus of the subalgebra U_q(su(2)) for calculation of
Clebsch-Gordan coefficients (CGCs) of the quantum algebra U_q(su(3)). The key
formulas of the method are couplings of the tensor and projection operators and
also a tensor form for the projection operator of U_q(su(3)). We obtain a very
compact general analytical formula for the U_q(su(3)) CGCs in terms of the
U_q(su(2)) Wigner 3nj-symbols.Comment: 9 pages, LaTeX; to be published in Yad. Fiz. (Phys. Atomic Nuclei),
(2001
Quantum deformations of D=4 Euclidean, Lorentz, Kleinian and quaternionic o^*(4) symmetries in unified o(4;C) setting
We employ new calculational technique and present complete list of classical
-matrices for complex homogeneous orthogonal Lie algebra
, the rotational symmetry of four-dimensional
complex space-time. Further applying reality conditions we obtain the classical
-matrices for all possible real forms of :
Euclidean , Lorentz , Kleinian
and quaternionic Lie algebras.
For we get known four classical Lorentz -matrices,
but for other real Lie algebras (Euclidean, Kleinian, quaternionic) we provide
new results and mention some applications.Comment: 13 pages; typos corrected. v3 matches version published in PL
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