Gauge transformations in relativistic two-particle constraint theory

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 ${\alpha }^2/r^2$, leading to a gauge invariant critical coupling constant ${\alpha }_c=1/2$.

32 pages, latex file with 3 figures, uses epsfile.sty for figures

References in corpus (4)

• The two-fermion relativistic wave equations of Constraint Theory in the Pauli-Schrödinger form
• The relativistic two-body potentials of constraint theory from summation of Feynman diagrams
• The two-fermion vector potential of constraint theory from Feynman diagrams
• Strongly coupled positronium in a chiral phase

Cited by in corpus (3)

• Singularity Structures in Coulomb-Type Potentials in Two Body Dirac Equations of Constraint Dynamics
• Relativistic Calculation of the Meson Spectrum: a Fully Covariant Treatment Versus Standard Treatments
• Applications of Two-Body Dirac Equations to the Meson Spectrum with Three versus Two Covariant Interactions, SU(3) Mixing, and Comparison to a Quasipotential Approach