Particle Position in Quantum Field Theories

O. Steinmann

Tracy Lupher

There are significant problems involved in determining the ontology of quantum field theory (QFT). An ontology involving particles seems to be ruled out due to the problem of defining localized position operators, issues involving interactions in QFT, and, perhaps, the appearance of unitarily inequivalent representations. While this might imply that fields are the most natural ontology for QFT, the wavefunctional interpretation of QFT has significant drawbacks. A modified field ontology is examined where determinables are assigned to open bounded regions of spacetime instead of spacetime points.

Jeroen C. Vink

Nuno Barros e Sá, Cláudio Gomes

Abstract The purpose of this article is to construct an explicit relation between the field operators in Quantum Field Theory and the relevant operators in Quantum Mechanics for a system of N identical particles, which are the symmetrised functions of the canonical operators of position and momentum, thus providing a clear relation between Quantum Field Theory and Quantum Mechanics. This is achieved in the context of the non-interacting Klein–Gordon field. Though this procedure may not be extendible to interacting field theories, since it relies crucially on particle number conservation, we find it nevertheless important that such an explicit relation can be found at least for free fields. It also comes out that whatever statistics the field operators obey (either commuting or anticommuting), the position and momentum operators obey commutation relations. The construction of position operators raises the issue of localizability of particles in Relativistic Quantum Mechanics, as the position operator for a single particle turns out to be the Newton–Wigner position operator. We make some clarifications on the interpretation of Newton–Wigner localized states and we consider the transformation properties of position operators under Lorentz transformations, showing that they do not transform as tensors, rather in a manner that preserves the canonical commutation relations. From a complex Klein–Gordon field, position and momentum operators can be constructed for both particles and antiparticles.

samir dzolota

In the realm of theoretical physics, a long-standing challenge remains: reconciling the fundamental principles of quantum mechanics with the nature of spacetime and gravity. This article explores the relationship between my proposed Unified Energy Exchange Framework (UEE) and Quantum Field Theory (QFT). While QFT provides a powerful framework for describing interactions and fields at the quantum level, it falls short of explaining the origin of the quantum fields themselves and their fundamental properties, such as superposition. This work posits that energy exchange between dual particles, as described in my framework, offers a deeper understanding of both the emergence of quantum fields and their superposition, addressing the gaps left by QFT.

Paul Teller