87 research outputs found
Superintegrable models of Winternitz type
A general procedure is outlined which allows one to construct superintegrable
models of Winternitz type. Some examples are presented.Comment: 6 pages, LaTeX; To appear in Phys. Lett.
The Quantum Galilei Group
The quantum Galilei group is defined. The bicrossproduct
structure of and the corresponding Lie algebra is revealed. The
projective representations for the two-dimensional quantum Galilei group are
constructed.Comment: AMSTe
Superintegrable Calogero-type systems admit maximal number of Poisson structures
We present a general scheme for constructing the Poisson structure of
super-integrable dynamical systems of which the rational Calogero-Moser system
is one of the most interesting one. This dynamical system is dimensional
with first integrals and our construction yields degenerate
Poisson tensors that each admit Casimirs. Our results are quite
generally applicable to all super-integrable systems and form an alternative to
the traditional bi-Hamiltonian approach
Global Space-Time Symmetries of Quantized Euclidean and Minkowski Superspaces
Starting with assumptions both simple and natural from "physical" point of
view we present a direct construction of transformations preserving wide class
of (anti)commutation relations which describe Euclidean/Minkowski superspace
quantizations. These generalized transformations act on deformed superspaces as
the ordinary ones do on undeformed spaces but they depend on non(anti)commuting
parameters satisfying some consistent (anti)commutation relations. Once the
coalgebraic structure compatible with the algebraic one is introduced in the
set of transformations we deal with quantum symmetry supergroup. This is the
case for intensively studied so called N=1/2 supersymmetry as well as its three
parameter extension. The resulting symmetry transformations - supersymmetric
extension of theta-Euclidean group can be regarded as global counterpart of
appropriately twisted Euclidean superalgebra that has been shown to preserve
N=1/2 supersymmetry.Comment: 34 pages; this is the final version accepted for publication in JHE
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