Quantization with Infinite Classical Fields: The Quantum/Classical Correspondence

It is shown that quantization of an external field apart of being intrinsic in quantum field theories, it can be also done in a fully scenario of classical electrodynamics. In this paper the quantization of field is demonstrated that is dual in the sense that not only is exclusive from quantum mechanics, but also in classical electrodynamics. To accomplish this, the Dirac-Delta function is derived because in according to Feynman rules, the argument gives direct information on the conservation of momentum and energy of particles under interaction. Thus, in scenarios of interaction with strong laser, apart that nonlinear Compton scattering is identified, that classical electrodynamics can arrive to same results.