Massless Wave States of Two-Fermion Systems - High Energy Physics - TheoryReport as inadecuate

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Abstract: It is known that in the ladder approximation the relativistic two-fermionbound-state equation of Bethe and Salpeter has solutions corresponding to thebinding energy equal to the total mass of the particles. The study of thesemassless states has been carried out only for the bound system at rest. Ofcourse, such composite boson can not be in the state of rest. But it is moreimportantly that this approach for the massless boson can not be interpreted asthe limiting case of a nonzero mass system because the phase velocity of theboson wave must equal to the speed of light. Using the Bethe-Salpeter equationin the ladder approximation, we have obtained the wave equation for themassless bound states of two fermions with equal masses and the electromagneticinteraction between them. Neglecting retardation of the interaction, solutionscorresponded to the stationary wave states of the composite boson, have beenfound. The boson wave function can be represented as an infinite, straightthread, the transverse radius of which is more than the Compton wavelength ofthe fermion. Two energy branches of the bosons with quantized energies havebeen determined. The appearance of these branches is due to the strongrenormalization of the fine structure constant for the massless states.

Author: A.I. Agafonov Russian Research Center Kurchatov Institute



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