On the uniqueness of the expected stress-energy tensor in renormalizable field theories

TL;DR

This paper discusses the limited ambiguity in the expected stress-energy tensor in four-dimensional renormalizable quantum field theories, showing that renormalization ambiguities are confined to local polynomial actions of dimension four.

Contribution

It demonstrates that the ambiguity in the expected stress-energy tensor due to renormalization is restricted to local polynomial actions of canonical dimension four.

Findings

Ambiguity in the stress-energy tensor is limited to local polynomial actions.

Renormalization ambiguities are constrained by the structure of the effective action.

The allowed ambiguity is severely restricted by the theory's dimensionality.

Abstract

It is argued that the ambiguity introduced by the renormalization in the effective action of a four-dimensional renormalizable quantum field theory is at most a local polynomial action of canonical dimension four. The allowed ambiguity in the expected stress-energy tensor of a massive scalar field is severely restricted by this fact.