Scalar Quantum Field Theory in Disordered Media

TL;DR

This paper studies a scalar quantum field in disordered media with random coefficients, deriving the Green's function and revealing a similarity to self-interacting theories with frequency-dependent coupling.

Contribution

It introduces a model of scalar quantum fields in disordered media with Gaussian randomness and computes the Green's function up to one-loop order.

Findings

Green's function obtained for the disordered scalar field

Disordered theory resembles a self-interacting $bb4$ theory

Frequency-dependent coupling emerges in the effective theory

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 an annealed-like disordered medium, modeled by centered stationary and Gaussian processes, is analyzed. After performing the averages over the random functions, we obtain the two-point causal Green's function of the model up to one-loop. The disordered scalar quantum field theory becomes qualitatively similar to a $\lambda\phi^{4}$ self-interacting theory with a frequency-dependent coupling.