Particle Localization in Relativistic Quantum Physics

There is no such thing as a covariant position operator in relativistic quantum theory, and I would like to know why.

I do of course have some answers to this question, and at times I have even found these answers fully satisfying. In my Ph.D Thesis I developed a reasonably deep-seated one. Some of this material was published in my:

  • "The Negative Energy Sea", in The Philosophy of Vacuum, S. Saunders and H. Brown (eds.), Oxford: Clarendon Press (1991), p.65-110.
  • However, I still thought there remained a severe problem in accounting for the locality of the objects that we do in fact see in the laboratory: something is localized, after all. How do we explain it - and what is it? For a statement of this latter problem, see my:

  • "Locality, Complex Numbers, and Relativistic Quantum Theory", Proceedings of the Philosophy of Science Association, Vol.1, 1992, p.365-380.
  • This problem can be formulated in more general terms using the Reeh-Schlieder theorem. I was led to that by Malement's instructive criticism of Flemming's notion of hyperplane-dependent localization (which in the early '90s seemed to many to offer an attractive way out). For a statement of the problem in these terms, and for a possible solution to it, see my:

  • "A (Dis)solution of the Problem of Locality", Philosophy of Science (Proceedings), Vol.2, p.88-98 (1994).
  • Copyright Simon Saunders 2001. Last Updated: September 16 2001.