From quantum field theory to quantum mechanics

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Sa, NBE (Author) Other; Gomes, C (Author) FCUP

Journal

Title: European Physical Journal C

Vol. 81

ISSN: 1434-6044

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 3 Citations

Other information

Authenticus ID: P-00V-MEJ

DOI: 10.1140/epjc/s10052-021-09742-0

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 11