Renormalization: the observable-state model Part II

TL;DR

This paper presents a novel approach to renormalization in quantum field theory by reformulating correlation functions as inner products of states and observables, allowing divergence removal via projectors without counterterms.

Contribution

It introduces a new observable-state model for phi^4 theory that replaces traditional renormalization with a projector method to handle divergences.

Findings

Divergences are linked to partial traces over internal vertices.

Finite correlation functions are obtained without counterterms.

The approach offers a new perspective on renormalization in QFT.

Abstract

The purpose of this work is to rewrite the generating functional of phi^4 theory for the n = 0 and n = 4 correlation functions as the inner product of a state with an observable, as we did in [J. S. Ardenghi, M. Castagnino, Phys. Rev. D, 85, 025002, (2012)] for the two-points correlation function. The observables are defined through the external sources and the states are defined through the correlation function itself. In this sense, the divergences of Quantum Field Theory (QFT) appear in the reduced state by taking the partial trace of the state with respect to the internal vertices that appear in the perturbation expansion. From this viewpoint, the renormalization can be substituted by applying a projector on the internal quantum state. The advantage of this new insight is that we can obtain finite contributions of the correlation functions without introducing counterterms in the Lagrangian or by manipulating complex divergent quantities.