text: A full description of non-linear inverse Compton scattering must include some effects related to the quantization of light and matter. The principal ones are listed below.
  * Inclusion of the discretization of the emitted radiation, i.e. the introduction of photons with respect to the continuous description of the classical limit. This effect does not change quantitatively the emission features but changes how the emitted radiation is interpreted. A parameter equivalent to  can be introduced for the photon of frequency  and it is called photon quantum parameter:where  is the photon four-wavevector and  is the three-dimensional wavevector. In the limit in which the particle approaches the speed of light, the ratio between  and  is equal to:From the Frequency distribution of radiated energy one can get a rate of high-energy photon emission distributed in  as a function of  and  but still valid in the classical limit:
  where  stands for the McDonald functions. The mean energy of the emitted photon is given by . Consequently, a large Lorentz factor and intense fields increase the chance of producing high-energy photons.  goes as  because of this formula.
  * The effect of radiation reaction, due to photon recoil.  The electron energy after the interaction process reduces because part of it is delivered to the emitted photon and the maximum energy achievable by the emitted photon cannot be higher than the electron kinetic energy. This effect is not taken into account in non-linear Thomson scattering in which the electron energy is supposed to remain almost unaltered in energy such as in elastic scattering. Quantum radiation reaction effects become important when the emitted photon energy approaches the electron energy. Since  ,  if  the classical limit of NICS is a valid description, while for  the energy of the emitted photon is of the order of the electron energy and photon recoil is very relevant.
  * The quantization of the motion of the electron and spin effects. An accurate description of non-linear inverse Compton scattering is made considering the electron dynamics described with the Dirac equation in presence of an electromagnetic field.