Hello to all:

I'd like to get some advice on a problem I am presently considering.

Let's consider a Dirac spinor u(p), and for a concrete example, let's
take the u^(1) for an spin up electron, where N is the usual
normalization factor:

/ 1 \
| 0 |
u^(1)=N | p_z / E+m | (1)
\ p_+/E+M /

To place this "at rest," we set p=0 and E=m, so that:

/ 1 \
| 0 |
u^(1)=N | 0 | (2)
\ 0 /

But, because of the uncertainty principle:

delta t delta E >= (1/2) hbar (3a)
delta x delta p >= (1/2) hbar (3b)

there is really no such thing as a "zero" momentum p=0, or E=m, only
the expected values <p>=0, <E>=m. How, therefore, might one write
u^(1) for an electron "at rest," in light of uncertainty?

Specifically, can we ever really have the state (2) in light of
Heisenberg, or, does one need to take the p and E in (1) and use in
their place, the expected values <p> and <E>, and / or the Root mean
square deviations delta p and delta E? For example, might one use, at
rest:

E --> m +/- delta E (4a)
p --> 0 +/- delta p (4b)

or some such expression other than p=0, or E=m.

Thanks.

Jay.
____________________________
Jay R. Yablon
Email: jyablon@nycap.rr.com
co-moderator: sci.physics.foundations
Weblog: http://jayryablon.wordpress.com/
Web Site: http://home.nycap.rr.com/jry/FermionMass.htm
By the way, I think the first step is to recognize that E and p make