Re: QED Reformulation

[Bob_for_short]

I, as the author of a "reformulation" approach, am interested in a
constructive feedback from researchers capable of understanding the
issues in question and interested in resolving the old physical
problems in quantum electrodynamics.

My articles with ideas and results are currently the following:
<< Atom as a "Dressed" Nucleus >>, CEJP, V. 7, N. 1, pp. 1-11 (2009),
available also on-line at http://arxiv.org/abs/0806.2635,

and

<< Reformulation instead of Renormalizations >>, http://arxiv.org/abs/0811.4416.

My approach is based on a new physical insight about coupling a charge
and its radiated electromagnetic field. Briefly, in my construction it
is not possible to "decouple" them since they are different features
of one compound system. Mathematically "mechanical" and "wave"
variables are just separated variables of one complex system - an
"electronium". Doing so, we can preserve the energy-momentum
conservation laws in course of radiation without introducing a "self-
action" ansatz, even in CED. As well, such coupling is permanent and
does not need to be treated perturbatively - the electromagnetic waves
are emitted automatically and unavoidably. Thus no UV and IR problems
arise in such a construction. It is an interesting opportunity of
building a self-consistent theory without conceptual, physical, and
mathematical difficulties.

Feel free to discuss and contribute to developing this direction. I
count on constructive participation of interested physicists.

Regards,

Vladimir Kalitvianski.

[meopemuk]

Hi Vladimir,

thank you for opening this discussion forum. We have discussed your
approach a while ago. So, I will only summarize a few points here.

First, I agree with almost everything you said when criticizing the
traditional renormalization approach to QFT. Definitely, we need a
better theory in which the definition of particles is not affected by
renormalization. However, I don't see a good reason why your
"electronium" approach should be regarded as a successful alternative
to QED.

1. You propose a new Hamiltonian of QED in eq. (60) of "Reformulation
instead of renormalizations". The first question is: where did you get
this Hamiltonian from? As far as I can see, you have not derived it
from any general principle. The bulk of the paper contains discussions
of some classical oscillators. They are supposed to serve as an
analogy for the coupling of electrons with EM field. Perhaps, I lack
imagination, but I don't see a connection between masses on springs
and electron-photon interaction. So, I cannot buy your analogies. Let
us then assume that you've simply postulated the Hamiltonian (60) and
move on.

2. The next challenge is to understand how exactly this Hamiltonian
looks like. We are dealing with a system having a variable number of
particles, so the Hamiltonian must involve some creation and
annihilation operators. However, they are not written explicitly.
Perhaps they are contained in your symbols \pi_c and u_c? But I
couldn't find what these symbols mean exactly. What is H_osc? If you
want a serious discussion, you should explain exactly the meaning of
all mathematical symbols in your formulas.

3. OK, let us assume that we got the Hamiltonian. The only way to
convince a physicist that this is the correct Hamiltonian is to
perform calculations and show some agreement with experiment. This is
where your approach is most vulnerable. You mention that your approach
describes the Lamb shift "without problem", but there is no proof. But
let us not even talk about difficult stuff, like anomalous magnetic
moment or Lamb shift. I would be happy to see at least the simple
bound state of the hydrogen atom. Can I see from your Hamiltonian (60)
that the binding energy of "electronium" and "protonium" is ~13.6 eV?

4. Can you calculate some simple scattering cross-sections and compare
them with experiments?

Your approach could be correct and revolutionary, but you failed to
win me on your side. In your presentation you rely too much on
analogies, intuition and handwavings. In my opinion, it would be
better to stick to hard-core math and explore all possible comparisons
with experimental data. Then, perhaps, you can prove me wrong.

Regards.
Eugene.

[Vladimir Kalitvianski]

On 11 sep, 03:33, meopemuk <eugene_stefanov...@usa.net> wrote:

> Hi Vladimir,
> thank you for opening this discussion forum. We have discussed your
> approach a while ago. So, I will only summarize a few points here.
> First, I agree with almost everything you said when criticizing the
> traditional renormalization approach to QFT. Definitely, we need a
> better theory in which the definition of particles is not affected by
> renormalization. However, I don't see a good reason why your
> "electronium" approach should be regarded as a successful alternative
> to QED.

Let me explain it in two words. The mass renormalization appeared
first in CED where the energy-momentum conservation laws were proposed
to be preserved via self-action of an electron on itself. I propose to
look at the "mechanical" equations as at describing the center of
inertia of a compound system rather than as the electron personal
coordinates. Is it physically acceptable? Is it justified? I think
yes. Factually any material body has "internal" degrees of freedom
(oscillators or not) and we "observe" the body thanks to exchange with
these internal degrees of freedom. Why we should think differently for
an electron? Especially if the "self-action" approach fails badly.

The advantage of "electronium" is in naturally and permanently
coupling the charge and the field degrees of freedom. It is quite
physical as it correspond to reality. Considering this coupling
perturbatively is not necessary. Thus we have a much better initial
approximation where an essential part of interaction is already taken
into account. We obtain the soft radiation immediately in the first
Born approximation, as it should be.

> 1. You propose a new Hamiltonian of QED in eq. (60) of "Reformulation
> instead of renormalizations". The first question is: where did you get
> this Hamiltonian from? As far as I can see, you have not derived it
> from any general principle. The bulk of the paper contains discussions
> of some classical oscillators. They are supposed to serve as an
> analogy for the coupling of electrons with EM field. Perhaps, I lack
> imagination, but I don't see a connection between masses on springs
> and electron-photon interaction. So, I cannot buy your analogies. Let
> us then assume that you've simply postulated the Hamiltonian (60) and
> move on.

Let us forget about (60) for instance. Let us decide if the physical
idea of a compound system "electronium" is acceptable? Is an electron
a part of a compound system in reality? If so, then we can go father.

> What is H_osc?

It is a usual QED oscillator Hamiltonian:

H_osc = sum_k {h-bar*omega_k * a^+_k * a_k}

in terms of creation operators. In terms of P and Q it is a sum of QM
oscillators with known wave functions. In electronium they stand for a
wave function describing the relative motion in a compound system,
just like psi_n(r) in the Hydrogen atom or a Slater determinant
psi_n(r1,r2,...,rN) in an N-electron atom/ion.

Photons are described with quantum oscillators. How can one excite
an oscillator? By an external driving force acting on what? On a part
of this oscillator. As soon as an external force acts on the electron
and this makes the oscillator excite, the electron is a part of the
oscillator. Ensemble of all possible photon oscillators + electron is
a compound system that I call an electronium. The mechanical part of
my article explains how this system works. As soon as the energy-
momentum conservation law is implemented in a physical way, I think we
have now a good model for electrodynamics: everything in terms of
physical entities and their potential interactions.

I invite you to read carefully this part because it is the energy-
momentum that was implemented badly in CED. Of course, we have a non-
elementary system now but with "elementary" quasi-particles - CI and
oscillators. The equations for quasi-particles may be casted in a
covariant form, as explained in the article of I.V. Polubarinov.

[Eugene Stefanovich]

-----Original Message-----
From: qed-refo...@googlegroups.com [mailto:qed-refo...@googlegroups.com] On Behalf Of Vladimir Kalitvianski
Sent: Saturday, October 09, 2010 7:53 AM
To: QED Reformulation
Subject: Re: QED Reformulation

> I think we
> have now a good model for electrodynamics: everything in terms of
> physical entities and their potential interactions.

If you believe so, then go ahead and use your theory to calculate some predictions that can be compared with experiment: energy spectra, scattering cross-sections, light emission intensities, etc. The only reliable way to earn acceptance of your theory is to make some non-trivial prediction and convince experimentalists to confirm it. You have a lot of work ahead of you. Good luck.

Eugene.

[Vladimir Kalitvianski]

On 9 oct, 22:43, Eugene Stefanovich <Eugene.Stefanov...@synopsys.com>
wrote:

>
> > I think we
> > have now a good model for electrodynamics: everything in terms of
> > physical entities and their potential interactions.
>
> If you believe so, then go ahead and use your theory to calculate
> some predictions that can be compared with experiment: energy spectra,
> scattering cross-sections, light emission intensities, etc. The only
> reliable way to earn acceptance of your theory is to make some non-trivial
> prediction and convince experimentalists to confirm it. You have a lot of
> work ahead of you. Good luck.

Hi Eugene,

You are right, of course.

Let us see what we already have in terms of spectra. My estimations
correspond to the pioneering work of T. Welton who obtained a good
number for the Lamb shift.

Let us see what we already have in terms of anomalous magnetic moment.
Again, in a non-relativistic case one can obtain the right order but
the opposite sign for the magnetic moment in Hydrogen. So the effect
exists but is comparable with the neglected relativistic contributions
(see T. Welton's seminal article).

Let us see what we already have in terms of cross sections. Here we
have immediately soft radiation in the first Born approximation. This
is a correct physical effect which is obtained in the standard QED
after heavily infrared problem resolving.

This all means we have a good physical approach. Everything is
obtained directly and naturally. Of course, we need to carry out
relativistic calculations. It is a professional work thatI cannot
afford for instance.

You did not tell me whether you consider the idea of electronium
reasonable or it is a completely strange construction in your eyes.
Can you share your opinion about it basing on the non-relativistic
estimations already available?

[Vladimir Kalitvianski]

On 9 oct, 22:43, Eugene Stefanovich <Eugene.Stefanov...@synopsys.com>
wrote:

> The only reliable way to earn acceptance of your theory is
> to make some non-trivial prediction and convince experimentalists
> to confirm it.

No, my primary goal is to construct a physically acceptable theory,
without bare stuff, counter-terms, etc., rather than to predict
something unusual. Kind of a short-cut to the final (renormalized and
IR fixed) QED results.

[Eugene Stefanovich]

In my personal opinion I don't find your electronium idea attractive.
But this should not slow you down. As I said: go ahead, develop your theory, compare it with experiment.
Perhaps one day you'll prove that I am wrong and you are right.

Eugene.

-----Original Message-----
From: qed-refo...@googlegroups.com [mailto:qed-refo...@googlegroups.com] On Behalf Of Vladimir Kalitvianski
Sent: Saturday, October 09, 2010 2:16 PM
To: QED Reformulation
Subject: Re: QED Reformulation

[Vladimir Kalitvianski]

On 9 oct, 23:26, Eugene Stefanovich <Eugene.Stefanov...@synopsys.com>
wrote:

> In my personal opinion I don't find your electronium idea attractive.

OK, can you tell what is not attractive? (In fact, it should not be
attractive but physical, in my opinion.)

Tell me, can en electron be a part of oscillators?

By the way, how is your research going?

[Vladimir Kalitvianski]

From discussion of L. Motl's blog entry "Quantum field theory has no
problems" (http://motls.blogspot.com/2010/11/quantum-field-theory-has-
no-problems.html).


Dear Lubos,

In my opinion, the problem of QEDis in admitting self-action in jA
( => infinite potential energy) and in awkwardly written interaction
(permanently coupled things are decoupled in the initial
approximation).

Counter-terms cancel the self-energy contributions, and selective
summation of IR diagrams restores the permanent coupling effect (soft
radiation). Why not start from a "repaired" Hamiltonian for the very
beginning? Difficult to construct it? No, let us try at least!

[Vladimir Kalitvianski]

From Lubos Motl:
-------------------------
Dear Vladimir, the QED Hamiltonian is the perfect Hamiltonian you can
write with those fields - the only renormalizable interacting gauge-
invariant Hamiltonian/Lagrangian with the gauge field and a charged
Dirac field. There is no way to modify it without spoiling either
gauge invariance or renormalizability or something else. Cheers, LM
--------------------------------


I understand your worry but there are gauge-invariant formulations of
QED (in terms of Dirac's variables, for example) which can be
corrected without spoiling reasonable features. For example, I
introduce a formula for r expressed via R and radiated field strengths
e_k which all are gauge invariant variables. The starting point for
equation modification is the Coulomb gauge which is called also
"radiation gauge" and is gauge invariant (contains only transversal
field strengths e_k).