Auxiliary fields and linear response in Lagrangian many body theory

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Abstract
A brief discussion is presented of the use of auxiliary field techniques in a functional integral formulation of many body theory. By using a Lagrangian representation for the Green functions from the outset a description is obtained in which true and auxiliary fields are treated on a more nearly equal basis than in partition function methods. The interacting fields are shown to have physical significance, their propagators leading to linear response functions of the true system. A diagrammatic representation analogous to that of a true interacting field problem is shown to follow in a straightforward manner. Transformations among fields are considered.

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