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The spatial formation of coherent random laser modes in strongly scatteringdisordered random media is a central feature in the understanding of thephysics of random lasers. We derive a quantum field theoretical method forrandom lasing in disordered samples of complex amplifying Mie resonators whichis able to provide self-consistently and free of any fit parameter the full setof transport characteristics at and above the laser phase transition. Thecoherence length and the correlation volume respectively is derived as anexperimentally measurable scale of the phase transition at the laser threshold.We find that the process of stimulated emission in extended disorderedarrangements of active Mie resonators is ultimately connected to time-reversalsymmetric multiple scattering in the sense of photonic transport while thediffusion coefficient is finite. A power law is found for the random laser modediameters in stationary state with increasing pump intensity.

A Self-Consistent Quantum Field Theory for Random Lasing