Newton-Wigner localization

Newton-Wigner localization is a scheme for obtaining a position operator for massive relativistic quantum particles. It is known to largely conflict with the Reeh-Schlieder theorem outside of a very limited scope.

External links

* [http://philsci-archive.pitt.edu/archive/00000098/00/segal.pdf Academic paper discussion Newton-Wigner localization in relation to Reeh-Schlieder theorem]

The Newton Wigner position operators x₁ , x₂, x₃, are the premier notion of positionin relativistic quantum mechanics of a single particle. They enjoy the same commutation relations with the 3 space momentum operators and transform underrotations in the same way as the x, y, z in ordinary QM. Though formally they have the same properties with respect top₁, p₂, p₃, asthe position in ordinary QM, they have additional properties. One of these is that $[x\_i\; ,\; ,\; p\_0\; ]\; =\; p\_i/p\_0$This ensures that the free particle moves at the expected velocity with the given momentum/energy. Apparently these notions were discovered when attempting to define a self adjoint operator in the relativistic setting that resembled the position operator in basic Quantum mechanics in the sense that at low momenta it approximately agreed with that operator. It also has several famous strange behaviors, one ofwhich is seen as the motivation for having to introduce quantum field theory.