Fully relativistic theory of the ponderomotive force in an ultraintense standing wave

A relativistic field-gradient (ponderomotive) force in a laser standing wave ceases to exist in a familiar form; e.g., the adiabatic Hamiltonian is not separable into kinetic and potential energies for electrons moving in the antinode planes. We show that the force in the direction across the initial motion of an electron reverses its sign and makes the high-field areas attractive for electrons, opposite to a regular ponderomotive force. The reversal occurs at a relativistic-scale incident momentum, and represents the only effect known so far that pins down a distinct borderline between relativistic and nonrelativistic motion.