Dear all,

The enduring discussion on some of my recently posted questions encourages me
to post the following question. (Thank you all!)

1) How the field variables are to be treated in a canonical theory of the
classical elm field?

Some books treat the vector potential, A(r,t), like the position
variable, so that the conjugated momentum reads

P_A = &L/&(&A/&t)

Is this appropriate?

2) What are the correct Hamiltonian eqs. of motion,

&P/&t = - &H/&Q,

or

&P/&t = - &H/&Q + &/&x &H/&(&Q/&x) ?

3) Which is the correct field Lagrangian? In many books, I see

L = E^2 - B^2

Heisenberg & Pauli (1929) and Fock & Podolsky (1932) used

2L = (E^2 - B^2) - (div A + &Phi/&t)

Thank you very much in advance!

Peter

In the original relativity theory of Poincaré and Lorentz, when a
clock and meterstick moves from one inertial frame of reference to
another, the clock ticks at a new rate and the meterstick changes
length but these changes are undetectable. That's a covariant theory.
I interpret an absolute yet undetectable frame of reference to be
equivalent to an axiom of space incommensurability and time
incommensurability.

To assert the converse, that clock rates and meterstick lengths don't
change and that time dilation is a mere consequence of a change in
perspective, is Einstein's theory.

The answer to the question, "Is Einstein's special theory derivable
from the original relativity theory of Poincaré and Lorentz?" seems to
be yes. It only requires a little redefinition and makebelieve,
right?

Shubee
http://www.everythingimportant.org/relativity/special.pdf

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
mass.

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.

http://jayryablon.files.wordpress.com/2008/07/foldy-wouthuysen-velocity-operator...

Perhaps more importantly, I have shown how the position operator may
developed, based not on a time parameter t, but on the Lorentz-invariant
physical proper time tau.

The usual argument for massless photons uses the Hamiltonian

H = (\sqrt (m^2c^4 + p^2c^2) ) (1)

and set (m = 0) to yield

H = pc

However, the original Hamiltonian (1) was derived using the next Legendre
transformation

H = pv - L = (\sqrt (m^2c^4 + p^2c^2) )

If alternatively we start assuming (v = c) in the transformation, the
result is

H = pc - L = pc (2)

where no assumption was taken about the mass.

Is this Hamiltonian (2) representing some kind of massive photon (somewhat
as in Proca theory [#]) or is really the same that (1)?

[#] http://en.wikipedia.org/wiki/Proca_action