5,447 research outputs found
Anyons, group theory and planar physics
Relativistic and nonrelativistic anyons are described in a unified formalism
by means of the coadjoint orbits of the symmetry groups in the free case as
well as when there is an interaction with a constant electromagnetic field. To
deal with interactions we introduce the extended Poincar\'e and Galilei Maxwell
groups.Comment: 22 pages, journal reference added, bibliography update
Heisenberg-type higher order symmetries of superintegrable systems separable in cartesian coordinates
Heisenberg-type higher order symmetries are studied for both classical and
quantum mechanical systems separable in cartesian coordinates. A few particular
cases of this type of superintegrable systems were already considered in the
literature, but here they are characterized in full generality together with
their integrability properties. Some of these systems are defined only in a
region of , and in general they do not include bounded solutions.
The quantum symmetries and potentials are shown to reduce to their
superintegrable classical analogs in the limit.Comment: 23 Pages, 3 figures, To appear in Nonlinearit
Superintegrability of the Fock-Darwin system
The Fock-Darwin system is analysed from the point of view of its symmetry
properties in the quantum and classical frameworks. The quantum Fock-Darwin
system is known to have two sets of ladder operators, a fact which guarantees
its solvability. We show that for rational values of the quotient of two
relevant frequencies, this system is superintegrable, the quantum symmetries
being responsible for the degeneracy of the energy levels. These symmetries are
of higher order and close a polynomial algebra. In the classical case, the
ladder operators are replaced by ladder functions and the symmetries by
constants of motion. We also prove that the rational classical system is
superintegrable and its trajectories are closed. The constants of motion are
also generators of symmetry transformations in the phase space that have been
integrated for some special cases. These transformations connect different
trajectories with the same energy. The coherent states of the quantum
superintegrable system are found and they reproduce the closed trajectories of
the classical one.Comment: 21 pages,16 figure
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