Abstract

An approach to the theory of Lorentz invariant distributions is developed in terms of covariant spectral representations. The behaviour of singular invariant distributions under a change of scale is analyzed. It is shown that the conventional extension of homogeneous singular functions into distributions inR 4, followed by a breakdown of homogeneity, is incomplete. Homogeneous extensions depending on an arbitrary scaling parameter are introduced, calculation techniques are developed and various formulae having applications in quantum field theory are derived.

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