Comment on the paper "Minimal Fields of Canonical Dimensionality are Free" [arXiv:1210.3864] by S. Weinberg

TL;DR

This note discusses that in scale-invariant relativistic field theories, fields of canonical dimensionality can exhibit interactions if scale invariance is spontaneously broken, challenging previous assumptions of their freeness.

Contribution

It clarifies the conditions under which fields of canonical dimensionality are interacting in spontaneously broken scale-invariant theories.

Findings

Fields of canonical dimensionality are not necessarily free when scale invariance is spontaneously broken.

Spontaneous breaking of scale invariance allows for interactions among canonical fields.

Challenges the previous notion that such fields must be free in scale-invariant theories.

Abstract

In this note we show that in a scale invariant relativistic field theory fields of canonical dimensionality are not necessarily free provided the scale invariance is spontaneously broken.