QED reformulation

[Chris Oakley]

Hi Vladimir,

Your work reminds me a bit of Eugene Stefanovich's "dressed particle"
approach. It is very different to what I am proposing, though. I would
like to say as little as possible about classical mechanics in
developing QED, and hence my emphasis on the underlying group theory.
I am also requiring explicit covariance. The decomposition of
Hamiltonian into a "free" part and an "interaction" may be necessary
as an approximation but cannot, in my view, be fundamental. I have a
theory of scattering processes so far and aim to be able to do bound
states, but have nothing substantial on those lines so far.

Best,

Chris Oakley

[Bob_for_short]

Dear Chris,

Thank you for joining this group!

On 11 sep, 00:18, Chris Oakley <coak...@cgoakley.demon.co.uk> wrote:

> Hi Vladimir,
>
> Your work reminds me a bit of Eugene Stefanovich's "dressed particle"
> approach.

We both speak of "dressed" electron but I write the "dressed" electron
solution explicitly so I know what it is. This solution contains
"mechanical" and "wave" variables together so it is a coupled electron
and its quantized EMF. This solution was advanced as ansatz but maybe
it could be obtained from a selective summation of interaction terms
on QED.

> It is very different to what I am proposing, though. I would
> like to say as little as possible about classical mechanics in
> developing QED, and hence my emphasis on the underlying group theory.
> I am also requiring explicit covariance.

It is good! It will come in handy for sure.

> The decomposition of
> Hamiltonian into a "free" part and an "interaction" may be necessary
> as an approximation but cannot, in my view, be fundamental.

I just would like to add that such decomposition determines non-
perturbed (not obligatorily free) Hamiltonian and perturbation. What I
do is taking into account the most essential "interaction" exactly.
This changes the initial approximation and the perturbative reminder
becomes physical. In particular, the permanent "coupling" of an
electron and its quantized EMF allows to describe the soft radiation
in the first Born approximation.

> I have a theory of scattering processes...

As fas as I can tell, your first Born approximation gives elastic
cross sections, without soft radiation. It is physically impossible.
That is why I believe we have to think of the ways of taking the most
essential "coupling" into account exactly. I proposed it as an ansatz,
as another understanding of what is what in electrodynamics.
Mechanical equations (3 coordinates) are good for the center of
inertia description, the wave equations are good for internal degrees
of freedom. Both mechanical and wave equations may be independent
(decoupled) in absence of external forces but they belong to one
compound system and take the corresponding part of the total work made
by an external force. Such interpretation excludes the harmful self-
action and describes well the radiation as well as CI trajectory.

The most important question is whether such understanding the
electrodynamics equation is physical, reasonable, acceptable, and
justified in you opinion. If yes, we may build Lagrangians and
Hamiltonians with these new entities as physical ingredients of our
theory. What do you think of all this?

Regards,

Vladimir.