Re: What is meant by "QED Reformulation"?

[Bob_for_short]

For those who are not aware of my motivation, here is a brief
explanation:

The standard QED equations can be obtained from the total QED
Hamiltonian H_tot which is a sum of "free" Hamiltonians of electrons,
positrons, and photons and an "interaction" Hamiltonian H_int:

H_tot = H_free + H_int. (1)

Everything in (1) was first implemented as physical and well defined
by QED fathers P. Dirac, W. Pauli, W. Heisenberg, to name some,
although in CED such a construction has non-physical solutions.

The interaction Hamiltonian was obtained from the interaction
Lagrangian density L_int = jA that includes the famous self-action.
The latter was intended to preserve the energy conservation law in
radiative processes. It is the self-action that led CED to non-
physical solutions so the energy conservation law was not preserved in
the exact equations in the end (due to exact runaway solutions).
Nevertheless the interaction term jA with the self-action was
introduced in QED (1) as well.

Elementary calculations showed that QED (1) cannot predict phenomena
that happen always: the soft radiation in the first Born approximation
whose probability is 1. As well (1) gives numerically meaningless
perturbative corrections that can be represented as "corrections" to
the fundamental constants (to masses and charges involved in (1)). The
natural conclusion is that (1) is a bad Hamiltonian implementing a bad
physics, similarly to CED. What to do then? Analise and advance a
better Hamiltonian, of course.

Presently the only known "way of repairing QED" is adding a "counter-
term" Hamiltonian H_counter-terms to (1) in order to subtract the
unphysical corrections to constants (= patching the Hamiltonian (1)
perturbatively):

(H_tot)_repaired = H_tot + H_counter-terms. (2)

In this "way" the original physical sense of the fundamental constants
is denied and (2) represents factually two non-physical addenda.
The fundamental constants are not treated as fundamental ones anymore
but as fitting (or "free"!) parameters. Factually nothing is physical
in (2): nor H_tot, neither H_counter-terms. In (2) we "build" a theory
from absolutely inexistent, non-physical stuff! Besides, the soft
radiation problem is not resolved with (2) automatically but needs an
additional and painful treatment.

What a physics is implemented in (1) if it needs immediately
"repairing"?

Many, knowing that after fitting to experiments, (2) predicts well
some experimental data, consider the situation to be satisfactory. But
nobody has been able to describe the real, physical electron is such a
QED so far! Sorry situation.

I consider this lucky "way" to be a too heavy and unnecessary price
for patching an obviously wrong Hamiltonian (1). In addition, the
renormalization ideology does not work in most cases (in quantum
gravity, for example) so it is not the right way to do physics at all.

On the other hand we must be conscious that renormalizations and
resolving the IR problem means changing the original Hamiltonian (1)
and corresponding "physics" in course of calculations. Yes, the
conceptual changes are done but not by advancing a new, physical
Hamiltonian from the beginning. "Reparation" is done in course of
calculations. As a result, it is not clear what we deal with in the
end.

It is known that renormalizations are nothing but discarding
(subtracting, "absorbing") corrections to the original fundamental
constants and this discarding changes the final results. The original
results are good for nothing; the renormalized and IR fixed ones are
good for calculations.

Thus there should be another Hamiltonian corresponding to the
renormalized results, and it is not the Hamiltonian (2) including non-
physical entities (bare particles and counter-terms). It is another
Hamiltonian involving only physical entities, say, dressed electrons,
positrons, photons and their interactions.

P. Dirac, R. Feynman and many other researchers pointed out that our
goal is finding (constructing) this better, physical Hamiltonian
H_tot_phys rather than patching (1). This is what I call a
"Reformulation" of a theory. It should give reasonable results
automatically, without appeal to non-existent entities (bare
electrons, their screening, etc.), without non-physical intermediary
results and excuses to get rid of them perturbatively.

I share this direction of doing physics and I hope to find
understanding in the research community because factually it is a very
desired and reasonable approach: you introduce some physical entities
and their interactions, and the result of interaction (scattering, for
example) is a change in populations of these physical entities
(numbers of photons and charges) and their energy-momenta. The
physics equations are to a great extent some balance equations and I
really believe that nothing non-physical and divergent should appear
in course of calculations if a theory is well formulated. I have
outlined a Novel QED Hamiltonian with its new physical entities in a
couple of articles.

[Bob_for_short]

Unhappiness with conceptual, physical, and mathematical problems in
QED was expressed by many researchers. Each does it in his own way.

I am saying this because I am not the only person who worries about
good physics and good mathematics. I can refer to Chris Oakley page
about QFT: http://www.cgoakley.demon.co.uk/qft/. There you can find
some citations from P. Dirac and R. Feynman. I know well that W. Pauli
was violently against renormalizations. Many know the phrase of L.
Landau: "The Hamiltonian is dead". It expresses a deep disappointment
with QFT. Generally, reformulation of a theory in better terms has
always been a dream of researchers, let us recognize it. Some people
are trying to do it within a given theory, see Eugene Stefanovich book
and references in it. Some advance new physical and/or mathematical
ideas to give some physical sense to the cut-off or to obtain loops
without divergences (remember supergravity by Wess-Zumino). I advanced
my ideas and constructions proceeding from my own research experience
and from knowledge obtained from literature. I stay withing QED's
physics. I just implement it better in my trial Hamiltonian. I see the
solution in correctly coupling charges and quantized EMF - coupling in
the frame of one compound system. Such coupling is permanent, thus no
adiabatic hypothesis is necessary and the soft radiation is obtained
automatically in the first Born approximation. Such coupling is
physical and different from unphysical self-action, thus no
corrections to the masses and charges arise. Finally, such coupling
smears quantum mechanically the charge interactions that make the
corresponding corrections small from the very beginning. I do not have
a "bare" + "counter-term" Lagrangian but a completely physical one. I
do not propose a poison + antidote as a "magic potion".

[Bob_for_short]

I am adding an article of I.V. Polubarinov on equations of quantum
electrodynamics, gauge invariance, and old quantization. It is
instructive to see how the Lorentz invariance may be implemented in
the Coulomb gauge. This article is available at

http://theor.jinr.ru/~pervush/articles/PhysPart3_03PolubarinovLO.pdf

so I think I do not violate copyrights.

In my approach I rebuild the QED Hamiltonian (A.25) from his review.