Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-09-16
J.Math.Phys. 38 (1997) 4951-4970
Physics
High Energy Physics
High Energy Physics - Theory
32 pages, latex file with 3 figures, uses epsfile.sty for figures
Scientific paper
10.1063/1.531957
Using connection with quantum field theory, the infinitesimal covariant abelian gauge transformation laws of relativistic two-particle constraint theory wave functions and potentials are established and weak invariance of the corresponding wave equations shown. Because of the three-dimensional projection operation, these transformation laws are interaction dependent. Simplifications occur for local potentials, which result, in each formal order of perturbation theory, from the infra-red leading effects of multiphoton exchange diagrams. In this case, the finite gauge transformation can explicitly be represented, with a suitable approximation and up to a multiplicative factor, by a momentum dependent unitary operator that acts in $x$-space as a local dilatation operator. The latter is utilized to reconstruct from the Feynman gauge the potentials in other linear covariant gauges. The resulting effective potential of the final Pauli-Schr\"odinger type eigenvalue equation has the gauge invariant attractive singularity $\alpha^2/r^2$, leading to a gauge invariant critical coupling constant $\alpha_c =1/2$.
Jallouli Hassen
Sazdjian Hagop
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