Interpolating between instant and light front dynamics

Abstract

The “instant” and “light front” forms of relativistic dynamics postulated by Dirac refer to physical conditions on flat spacelike surfaces in the Minkowski space. We consider another flat surface in the Minkowski space that upon parametric rotation interpolates between “instant” and “light front” surfaces. A projection of the covariant perturbation theory on the new surface is then considered. One limit of the theory reproduces the usual instant dynamics, whereas a different limit gives a light front dynamics. Neither infinite momemtum frame limit nor infinite momenta are involved. Although the interpolating surface is the “instant” surface in the moving system of reference, we argue why our procedure should not be associated with a Lorentz transformation.