Structure of quantum-mechanical relativistic two-body interactions for spinning particles |
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Authors: | H W Crater P Van Alstine |
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Institution: | (1) The University of Tennessee Space Institute, 37388 Tullahoma, Tennessee;(2) 12474 Sunny Glen Drive, 93021 Moorpark, California |
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Abstract: | Relativistic constraint mechanics yields consistent systems of coupled Dirac equations for pairs of spinning particles. We
explicitly connect these equations to the Bethe-Salpeter equation of quantum field theory and to the interactions of classical
Fokker-Tetrode dynamics (and hence to classical relativistic field theory) to obtain versions of these equations governed
by systems of (possibly noncoulombic) relativistic potentials whose detailed structures contain important relativistic effects
like correct Darwin interactions. We recast the defining pair of Dirac equations in a number of equivalent but important forms—“external
potential,” Sazdjian, hyperbolic, and Breit— and examine their interconnection. Since the potentials in these equations are
no more singular than — 1/4r2 we are able to solve appropriate versions of them nonperturbatively for the qˉq system to obtain a very good fit to the entire
meson spectrum and for the e
+
e
−
system to calculate the positronium spectrum of QED correct through order α
4
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Keywords: | |
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