On two constructions of an effective field theory

TL;DR

This paper compares two methods for constructing effective field theories from local interactions, demonstrating their equivalence and bridging traditional graphical renormalization with a newer inductive approach.

Contribution

It establishes the equivalence between the BPHZ graphical renormalization method and Costello's inductive construction for effective field theories.

Findings

Both constructions yield the same effective field theory.

The inductive method aligns with traditional graphical approaches.

The work bridges two different conceptual frameworks.

Abstract

In this paper we discuss two constructions of an effective field theory starting from a local interaction functional. One relies on the well-established graphical combinatorics of the BPHZ algorithm to renormalize divergent Feynman amplitudes. The other, more recent and due to Costello, relies on an inductive construction of local counterterms that uses no graphical combinatorics whatsoever. We show that these two constructions produce the same effective field theory.