1,283 research outputs found
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
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
A characterization of coboundary Poisson Lie groups and Hopf algebras
We show that a Poisson Lie group is coboundary if and only if the
natural action of on is a Poisson action for an appropriate
Poisson structure on (the structure turns out to be the well known ). We analyze the same condition in the context of Hopf algebras. Quantum
analogue of the structure on SU(N) is described in terms of generators
and relations as an example.Comment: 6 pages, PlainTeX, 2 (minor) typos corrected, to appear in
Proceedings of QG&QS, Banach Center in Warsaw, Nov. 199
Poisson structures on the Poincare group
An introduction to inhomogeneous Poisson groups is given. Poisson
inhomogeneous are shown to be coboundary, the generalized classical
Yang-Baxter equation having only one-dimensional right hand side. Normal forms
of the classical -matrices for the Poincar\'{e} group (inhomogeneous
) are calculated.Comment: 29 pages, LaTe
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