English

Localization of particles in quantum field theory

High Energy Physics - Theory 2010-12-20 v1 General Relativity and Quantum Cosmology High Energy Physics - Phenomenology Quantum Physics

Abstract

We put forward an interpretation of scalar quantum field theory as relativistic quantum mechanics by curing well known problems related to locality. A probabilistic interpretation of quantum field theory similar to quantum mechanics is difficult if particle localization is defined using the Newton-Wigner position operator as it is non-local and non-covariant. An alternative bilinear covariant position operator is discussed which incorporates a time operator that can be exponentiated to a unitary operator. Moreover, it satisfies an algebra that unifies special relativity and quantum mechanics and has the same form for particles with spin. Higher power position operators are derived which yield Heisenberg's uncertainty relations. Our ideas are illustrated with a relativistic wave function whose probability density can be perfectly localized.

Keywords

Cite

@article{arxiv.1012.3472,
  title  = {Localization of particles in quantum field theory},
  author = {W. Westra},
  journal= {arXiv preprint arXiv:1012.3472},
  year   = {2010}
}

Comments

23 pages

R2 v1 2026-06-21T16:59:26.314Z