Lagrangian theory with zero component. Application to the study of the polymers in solution (chains with exclued volume) and of the properties of electrons in a random potential

The Lagrangian theory of a field with n components can be generalized for values of n which are not integers and in particular for n=0. This extension is made by introducing ordered Green's functions. It is shown how the zero components Lagrangian theory can be used to describe the behaviour of an isolated polymer or of a solution of polymers with large molecular masses. It is remarked that by analytic continuation with respect to the coupling constant, it should be possible to study the properties of electrons in a random potential and perhaps the nature of the mobility edges