A statistical model for relativistic quantum fluids interacting with an arbitrary amplitude circularly polarized electromagnetic wave is developed in two steps. First, the energy spectrum and the wave function for a quantum particle (Klein Gordon and Dirac) embedded in the electromagnetic wave are calculated by solving the appropriate eigenvalue problem. The energy spectrum is anisotropic in the momentum K and reflects the electromagnetic field through the renormalization of the rest mass m to M=√m2+q2A2. Based on this energy spectrum of this quantum particle plus field combination (QPF), a statistical mechanics model of the quantum fluid made up of these weakly interacting QPF is developed. Preliminary investigations of the formalism yield highly interesting results - a new scale for temperature, and fundamental modification of the dispersion relation of the electromagnetic wave. It is expected that this formulation could, inter alia, uniquely advance our understanding of laboratory as well as astrophysical systems where one encounters arbitrarily large electromagnetic fields.