78 research outputs found
Quasi exactly solvable matrix models in sl(n)
We reconsider the quasi exactly solvable matrix models constructed recently
by R. Zhdanov. The 22 matrix operators representing the algebra sl(2)
are generalized to matrices of arbitrary dimension and a similar construction
is achieved for the algebra sl(n).Comment: LaTeX, 8 page
"Isochronic" dynamical systems and nullification of amplitudes
We construct the set of theories which share the property that the tree-level
amplitudes nullify even if both initial and final states contain the same type
of particles. The origin of this phenomenon lies in the fact that the reduced
classical dynamics describes isochronic systems.Comment: 12 pages, 3 figure
Lorentz transformations, sideways shift and massless spinning particles
Recently (Phys. Rev. Lett. 114 (2015), 210402) the influence of the so called
"Wigner translations" (more generally-Lorentz trans- formations) on circularly
polarized Gaussian packets ( providing the solution to Maxwell equations in
paraxial approximation) has been studied. It appears that, within this
approximation, the Wigner trans- lations have an efect of shifting the wave
packet trajectory parallel to itself by an amount proportional to the photon
helicity. It has been suggested that this shift may result from specific
properties of the algebra of Poincare generators for massless particles. In the
present letter we describe the general relation between transformation proper-
ties of electromagnetic field on quantum and classical levels. It allows for a
straightforward derivation of the helicity-dependent transforma- tion rules. We
present also an elementary derivation of the formula for sideways shift based
on classical Maxwell theory. Some comments are made concerning the
generalization to higher helicities and the relation to the coordinate operator
defined long time ago by Pryce.Comment: 13 pages; no figures; section "Conclusions" added; missing
normalization factor in eq.(20) inserted; final form to appear in Physics
Letters
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