Newton–Wigner localization (named after Theodore Duddell Newton and
Eugene Wigner
Eugene Paul "E. P." Wigner ( hu, Wigner Jenő Pál, ; November 17, 1902 – January 1, 1995) was a Hungarian-American theoretical physicist who also contributed to mathematical physics. He received the Nobel Prize in Physics in 1963 "for his con ...
) is a scheme for obtaining a
position operator
In quantum mechanics, the position operator is the operator that corresponds to the position observable of a particle.
When the position operator is considered with a wide enough domain (e.g. the space of tempered distributions), its eigenvalues ...
for massive
relativistic quantum particle
In quantum field theory, the energy that a particle has as a result of changes that it causes in its environment defines self-energy \Sigma, and represents the contribution to the particle's energy, or effective mass, due to interactions between ...
s. It is known to largely conflict with the
Reeh–Schlieder theorem outside of a very limited scope.
The Newton–Wigner position operators
1,
2,
3, are the premier notion of position
in relativistic quantum mechanics of a single particle. They enjoy the same
commutation relations with the 3 space momentum operators and transform under
rotations in the same way as the , , in ordinary
QM. Though formally they have the same properties with respect to
1,
2,
3, as
the position in ordinary QM, they have additional properties: One of these is that
:
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 of
which is seen as the motivation for having to introduce quantum field theory.
References
*
*
M.H.L. Pryce, ''Proc. Roy. Soc.'' 195A, 62 (1948)
*V. Bargmann and E. P. Wigner, ''Proc Natl Acad Sci USA'' 34, 211-223 (1948)
pdf
Quantum field theory
Axiomatic quantum field theory
{{quantum-stub