Structure of the Two-Point Function

Abstract

The two‐point functions of relativistic quantum field theory are discussed in the framework of distribution theory. A derivation in this framework of the Källén‐Lehmann representation is given. The singularities in x space are studied for the example of the D_P function. It is in general not possible to extract a singularity with support on the light cone. It is shown however that D_P is at best a measure in any neighborhood of the light cone. Thus Lehmann's statement that D_P is at least as singular as the corresponding free‐field function is confirmed.