Scalar quantum field theory in disordered media

Abstract

A free massive scalar field in inhomogeneous random media is investigated. The coefficients of the Klein-Gordon equation are taken to be random functions of the spatial coordinates. The case of a disordered medium modeled by centered stationary and Gaussian processes is analyzed. After performing the averages over the random functions, we obtain the two-point and the four-point Green's functions of the model up to one loop. The disordered scalar quantum field theory becomes qualitatively similar to a $\ensuremath{\lambda}{\ensuremath{\varphi}}^{4}$ self-interacting theory with a frequency-dependent coupling.