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Phase-Space Tensor Field Theory of Photon Transport: A Unifying Framework for Coherent and Incoherent Optics
Mykola Yaremenko
We present a novel theoretical frameworkthe Phase-Space Tensor Field Theory (PSTFT) that unifies the description of photon transport across quantum coherent, classical wave, and incoherent regimes. By introducing a photon state tensor Φμν(𝑥α, 𝑝β ) defined in an 8-dimensional phase space, our formulation simultaneously encodes spatiotemporal, spectral, and polarization degrees of freedom. The dynamics are governed by a geometrodynamic master equation that incorporates Hamiltonian evolution, decoherence, scattering, and nonlinear interactions. We demonstrate that PSTFT naturally reduces to Maxwell’s equations, radiative transfer theory, and geometric optics in appropriate limits, while enabling seamless transitions between quantum and classical descriptions. The theory introduces a new class of material parametersgeometric, decoherence, and scattering kernelsthat offer enhanced physical insight and computational efficiency for modern photonic systems. Applications include nonlinear and quantum optical phenomena, quantum light sources, complex media, integrated photonics, and nonimaging optics, where conventional theories fail to capture the full physical picture.
Keywords: Phase-space optics, tensor field theory, photon transport, geometric optics, coherence theory, Maxwell’s equations, nonlinear optics, quantum optics