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Stochastic mechanics for ponderomotive effect of a spin-less electron interacting with a high-intensity plane wave laser field

We discuss the relativistically covariant ponderomotive effect of a spin-less electron by a high-intensity laser field of a plane wave in the quantum regime. At first we recall the relativistic ponderomotive effect in classical mechanics. Then against that, we will investigate quantum mechanical expression of the ponderomotive effect by relativistic stochastic mechanics, where, we also propose relativistic stochastic mechanics to draw a trajectory of a spin-less electron. After giving a strict solution of stochastic mechanics, its slowly varying motion is examined as its ponderomotive effect in the quantum regime. Finally, we will see the universality of the ponderomotive effect acting on a spin-less electron interacting with a present high-intensity femtosecond laser, via the dressed (effective) mass of a spin-less electron bridging between classical and quantum mechanics.