Drift lagrangian for a relativistic particle in an intense laser field

The Lagrangian and Hamiltonian functions describing the average motion of a relativistic particle under the action of a slightly inhomogeneous intense laser field are obtained. In weak low-frequency background fields, such a particle on average drifts with an effective relativistically invariant mass, which depends on the laser intensity. The essence of the proposed ponderomotive formulation is presented in a physically intuitive and mathematically simple form yet represents a powerful tool for studying various nonlinear phenomena caused by the interaction of currently available smooth ultraintense laser pulses with plasmas.