1,635 research outputs found
Free motion on the Poisson SU(n) group
SL(N,C) is the phase space of the Poisson SU(N). We calculate explicitly the
symplectic structure of SL(N,C), define an analogue of the Hamiltonian of the
free motion on SU(N) and solve the corresponding equations of motion. Velocity
is related to the momentum by a non-linear Legendre transformation.Comment: LaTeX, 10 page
Extended phase space for a spinning particle
Extended phase space of an elementary (relativistic) system is introduced in
the spirit of the Souriau's definition of the `space of motions' for such
system. Our formulation is generally applicable to any homogeneous space-time
(e.g. de Sitter) and also to Poisson actions. Calculations concerning the
Minkowski case for non-zero spin particles show an intriguing alternative: we
should either accept two-dimensional trajectories or (Poisson) noncommuting
space-time coordinates.Comment: 12 pages, late
Phase spaces related to standard classical -matrices
Fundamental representations of real simple Poisson Lie groups are Poisson
actions with a suitable choice of the Poisson structure on the underlying
(real) vector space. We study these (mostly quadratic) Poisson structures and
corresponding phase spaces (symplectic groupoids).Comment: 20 pages, LaTeX, no figure
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