A brief review of Implicit Regularization and its connection with the BPHZ theorem

TL;DR

This paper reviews Implicit Regularization, a method that maintains calculations within physical dimensions, and discusses its compatibility with the BPHZ theorem, ensuring unitarity and locality in quantum field theory.

Contribution

It provides a concise overview of Implicit Regularization and demonstrates its compliance with the BPHZ theorem, highlighting its theoretical consistency.

Findings

Implicit Regularization stays within physical dimensions.

It respects unitarity and locality at all loop orders.

The method aligns with the BPHZ theorem's requirements.

Abstract

Quantum Field Theory, as the keystone of particle physics, has allowed great insights to deciphering the core of Nature. Despite its striking success, by adhering to local interactions, Quantum Field Theory suffers from the appearance of divergent quantities in intermediary steps of the calculation, which encompasses the need for some regularization/renormalization prescription. As an alternative to traditional methods, based on the analytic extension of space-time dimension, frameworks that stay in the physical dimension have emerged, Implicit Regularization is one among them. We briefly review the method, aiming to illustrate how Implicit Regularization complies with the BPHZ theorem, which implies that it respects unitarity and locality to arbitrary loop order.