Propagation of waves in a randomly inhomogeneous medium with strongly developed fluctuations. I. Renormalization group and $4-\varepsilon$-expansion

The standard quantum-field technique of the renormalization group and $4-\varepsilon$-expansions is applied to the problem of wave propagation in a randomly inhomogeneous medium. In the framework of the $4-\varepsilon$-expansion it is shown that for the dimensionless charge which characterizes the interaction with the noise field there exists an infrared-stable fixed point, all anomalous dimensions being expressible at this point in terms of known static exponents. However, analysis of the actual values of the parameters shows that the regime of critical scaling is not attained in real three-dimensional problems.