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arXiv · hep-th/9609117

Gauge transformations in relativistic two-particle constraint theory

H. Jallouli·H. Sazdjian
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Abstract

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-Schrödinger type eigenvalue equation has the gauge invariant attractive singularity $α^2/r^2$, leading to a gauge invariant critical coupling constant $α_c =1/2$.

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H. Jallouli, H. Sazdjian. 1996-09-16. Gauge transformations in relativistic two-particle constraint theory. https://doi.org/10.1063/1.531957

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