EFFECTIVE MEDIUM APPROXIMATION IN THE LOCALIZATION THEORY - SADDLE-POINT IN A LAGRANGIAN FORMULATION

A new method of studying the metal-insulator transition is proposed. All physical quantities are represented in terms of a field theory model in an extended space which consists of the real space and the space of supermatrices. The minimum of the effective Lagrangian describing the model gives equations coinciding with the corresponding equations derived before on the Bethe lattice and in high dimensionality. A concept of a function order parameter is discussed. In the saddle point approximation the density-density correlation function both in the metal and insulator regions is calculated. © 1990.