Braided structure of fractional Z3Z_3-supersymmetry

It is shown that fractional $Z_3$-superspace is isomorphic to the $q\to\exp(2\pi i/3)$ limit of the braided line. $Z_3$-supersymmetry is identified as translational invariance along this line. The fractional translation generator and its associated covariant derivative emerge as the $q\to\exp(2\pi i/3)$ limits of the left and right derivatives from the calculus on the braided lineComment: 8 pages, LaTeX, submitted to Proceedings of the 5th Colloquium `Quantum groups and integrable systems', Prague, June 1996 (to appear in Czech. J. Phys.

Colour lie algebras and R-matrices

The universal enveloping algebra of a colour Lie algebra is extended by a 'bosonization' process to a nongraded quasitriangular Hopf algebra, and the explicit form of the R-matrix for the Hopf algebra is found

q-exponential and q-gamma functions. II. q-gamma functions

For |q| ≠ 1, the integral definition of the gamma function in terms of the exponential function is generalized to a definition of a q-gamma function, or a family of q-gamma functions, in the standard and symmetric cases, using the q-exponential functions and their asymptotic behavior as z → ∞ on geometric sequences {zn(ζ) = qnζ} nεZ with common ratio q. The properties of the q-gamma functions (poles, zeros, product expansions) are also determined

Quasiclassical states of the Coulomb system and so(4, 2)

Quasiclassical bound states of the quantum mechanical Coulomb system are constructed. They are initially Barut-Girardello coherent states of the natural so(4, 2) dynamical algebra, and evolve in accordance with the Schrodinger equation. The asymptotic behaviour of expectation values and uncertainties of all the so(4, 2) observables is examined in detail for those states having a mean value of n, the principal quantum number, approaching infinity. There is no spreading with respect to these observables over times of the order of tau , the corresponding classical period, but the states do spread over times of the order of tau 6/. Periodic but successively weaker resurgences of coherence are found over times of the order of tau 3/. It is shown explicitly that the states are quasiperiodic over extremely long times