1,485 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
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
Some Comments on BPS systems
We look at simple BPS systems involving more than one field. We discuss the
conditions that have to be imposed on various terms in Lagrangians involving
many fields to produce BPS systems and then look in more detail at the simplest
of such cases. We analyse in detail BPS systems involving 2 interacting
Sine-Gordon like fields, both when one of them has a kink solution and the
second one either a kink or an antikink solution. We take their solitonic
static solutions and use them as initial conditions for their evolution in
Lorentz covariant versions of such models. We send these structures towards
themselves and find that when they interact weakly they can pass through each
other with a phase shift which is related to the strength of their interaction.
When they interact strongly they repel and reflect on each other. We use the
method of a modified gradient flow in order to visualize the solutions in the
space of fields.Comment: 27 pages, 17 figure
Field Theory on Quantum Plane
We build the defomation of plane on a product of two copies of
algebras of functions on the plane. This algebra constains a subalgebra of
functions on the plane. We present general scheme (which could be used as well
to construct quaternion from pairs of complex numbers) and we use it to derive
differential structures, metric and discuss sample field theoretical models.Comment: LaTeX, 10 page
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