Renormalization: the observable-state model

TL;DR

This paper introduces a decoherence-based renormalization method in quantum field theory that replaces traditional divergence subtraction with a Hilbert space projector, simplifying the formalism and extending applicability.

Contribution

It proposes a novel renormalization approach using decoherence formalism, addressing divergences through a Hilbert space projector, applicable even to non-renormalizable theories.

Findings

Eliminates divergences via a projector on a Hilbert subspace.

Maintains physical results of QFT with a more rigorous formalism.

Applicable to non-renormalizable quantum field theories.

Abstract

The usual mathematical formalism of quantum field theory is non-rigorous because it contains divergences that can only be renormalized by non-rigorous mathematical methods. The purpose of this paper is to present a method of subtraction of this divergences using the formalism of decoherence. This is achieved by replacing the standard renormalization method by a projector on a well defined Hilbert subspace. In this way a list of problems of the standard formalism disappears while the physical results of QFT remains valid. From it own nature, this formalism can be used in non-renormalizable theories.