The quarks and particles’ mass and mass/spin relations are provided with coordinates in configuration space and/or momentum space by means of the marriage of ordinary Poincaré group representations with a nonassociative algebra made through a demisemidirect product, in the notation of Leibniz algebras. Thus, we circumvent the restriction that the Poincaré group cannot be extended to a larger gr...

The propagation of light beams through astigmatic lens systems is accompanied by a transfer of orbital angular momentum. We develop a method to describe propagating light beams by operators of which the field is an eigenfunction. This method is applied to determine when an astigmatic lens system transforms gaussian beams into other gaussian beams and where in the system angular momentum is tran...

It is pointed out that if the molecular interpretation of the recently observed resonance X(3872) is valid, then nature may have prepared a good laboratory for us to examine the phenomenon of superradiance and subradiance of Dicke. The superradiance and supradiance factors are evaluated and the effects on the electromagnetic radiative decay of X(3872) are discussed. Our results using coordinate...

SO(p, q) = {g ∈ SLp+q(R) : g>Qg = Q} (where Q = ( 1p 0 0 −1q ) )  SU(2) −→ SO(3) SL2(R) −→ SO(2, 1) SU(2)× SU(2) −→ SO(4) SL2(C) −→ SO(3, 1) SL2(R)× SL2(R) −→ SO(2, 2) Sp∗(2, 0) −→ SO(5) Sp∗(1, 1) −→ SO(4, 1) Sp2(R) −→ SO(3, 2) SU(4) −→ SO(6) SL2(H) −→ SO(5, 1) SU(2, 2) −→ SO(4, 2) SL4(R) −→ SO(3, 3) Thus, these are small examples...

We perform the first long-time exploration of the classical dynamics of a driven billiard with a four-dimensional phase space. With increasing velocity of the ensemble, we observe an evolution from a large chaotic sea with stickiness due to regular islands to thin chaotic channels with diffusive motion leading to Fermi acceleration. As a surprising consequence, we encounter a crossover, which i...

The cross sections for photoand pion-induced production of baryon resonances and their partial decay widths to the two–body and multi–body final states are calculated in the framework of the operator expansion method. The approach is fully relativistic invariant, and it allows us to perform combined analyses of different reactions imposing directly the analyticity and unitarity constraints. All...