Dispersive Approach to the Trace Anomaly

Abstract

In the scalar $ϕ^4$ field model the dispersive approach to the trace anomaly is proposed. It is shown that it is impossible to get dispersion representation for all formfactors so that preserve both the translation and dilatation Ward identities. Subtractions which preserve energy-momentum conservation violate the classical trace Ward--Takahashi identity and give rise to an anomalous contribution to the matrix element of stress tensor $θ_μ^ν$. This contribution coincides with one-loop $β$-function in accordance with previous analyses based on RG technique.