Re: Might Foldy-Wouthuysen Transformations contain a Hidden Fermion Mass Generation Mechanism?


"kp" <4vector@xxxxxxxxx> wrote in message news:41c60118-c321-4922-b2f4-a9e240582f04@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx


Following this to its conclusion, this means that somewhere hidden in
the Foldy-Wouthuysen transformation, we have gone from a fermion which
is massless and luminous, to one which has a finite, non-zero rest mass
and travels at sub-luminous velocity. It seems, then, that it would be
important to specifically trace how the velocity operator of the
Dirac-Pauli representation with +/- c eigenvalues transforms into the
velocity operator (2) of Newton-Wigner which allows a continuous,
sub-luminous velocity spectrum, and at the same time, to trace through
how the rest mass goes from necessarily zero (with decoupled chiral
components), to non-zero with chiral couplings.

By doing so, perhaps one would find a mechanism for generating fermion
masses.

The Fermion of Dirac's equation is not massless, you can see the mass
right in the equation itself. Because the equation for velocity x=dx/
dt = +- c just means that this is not a well defined physically
meaningful operator. If would want to set the mass to zero in Dirac's
equation and then perform this transformation, you will start to
generate meaningless expressions and not a mass term.


kp

[Yablon]
Perhaps so, but just for the heck of it, I did a calculation of what happens to the mass matrix M=m.gamma^0 during the transformation from the Dirac-Pauli representation to the Newton-Wigner representation via Foldy-Wouthuysen. This is shown in:

http://jayryablon.wordpress.com/files/2008/06/foldy-wouthuysen.pdf

Not sure where to go from there, but I'll be away the rest of the week on vacation, so I'll take another look when I return.

Interested in any further thoughts you or others may have.

Best,

Jay.

.

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