Re: The Foldy-Wouthuysen Velocity Operator -- Is this Correct?

Jay R. Yablon schrieb:
There has been a fair amount of discussion on sci.physics.foundations in
the thread "Might Foldy-Wouthuysen Transformations contain a Hidden
Fermion Mass Generation Mechanism?" regarding the fact that the velocity
operator "alpha" of the Dirac Hamiltonian appears to suggest that a
fermion must travel at the speed of light, which some describe as making
"no sense."

While I had earlier thought that this might be the seat of a
mass-generation mechanism, I do not at this juncture believe that is the
case. In particular, as shown below, all rest masses cancel, and the
velocity then becomes amenable to distinct treatment independent of rest

In the 3-page file linked below, I have shown how this velocity operator
is (I think??) transformed into the Newton-Wigner representation using
the Foldy-Wouthuysen transformation, and how in that latter
representation, that velocity operator comes to make perfect sense.

For this connection, see the entry
S2h. Localization and position operators
in my theoretical physics FAQ at
For related information, see also
S2g. Particle positions and the position operato

Arnold Neumaier