Is Quantum Field Theory ontologically interpretable? On localization, particles and fields in relativistic Quantum Theory

TL;DR

This paper investigates the ontological interpretability of quantum field theory, analyzing localization schemes, the concept of particles, and their emergence from fields within a formal and conceptual framework.

Contribution

It introduces a formal criterion for particle admitance in quantum field theories and evaluates localization concepts, highlighting the emergent nature of particles from fields.

Findings

Naive localization fails due to Reeh-Schlieder theorem

Newton-Wigner localization violates microcausality

Particles are emergent phenomena from relativistic fields

Abstract

In this paper, I provide a formal set of assumptions and give a natural criterion for a quantum field theory to admit particles. I construct a na\"ive approach to localization for a free bosonic quantum field theory and show how this localization scheme, as a consequence of the Reeh-Schlieder theorem, fails to satisfy this criterion. I then examine the Newton-Wigner concept of localization and show that it fails to obey strong microcausality and thus is subject to a more general version of the Reeh-Schlieder theorem. I review approaches to quantum field theoretic explanations of particle detection events and explain how particles can be regarded as emergent phenomena of a relativistic field theory. In particular, I show that effective localization of Hilbert space vectors is equivalent to an approximate locality of observable algebras.