Does renormalization means discarding corrections to a known constant?

[Bob_for_short]

Your paper "Atom_CEJP.pdf" doesn't really tell me much more. You still reach a similar place near the end where you postulate a "relativistic" H_QED in eq(23), followed by a brief paragraph of insufficiently-justified statements.

I do not postulate but propose or advance my point of view. It means flexibility, if you like.

The purpose of this article is twofold: to present a good (working without fail) model of taking into account exactly the "vacuum field fluctuations" and then to propose a Novel QED Hamiltonian basing on the atomic example insight. I really hope that the "atomic" part of the article is not skipped by reader but studied with a pencil.

My ("insufficiently justified") statements are correct, this is the main point. I had no place to dive in details in the frame of one article. Yet I explained in words why it is so (form-factor influence). To demonstrate this, the non-relativistic cross section calculation is sufficiently detailed in it and its physics is quite eloquent. The relativistic calculation gives similar cross section properties. I agree that what is evident to me, may not be so evident to a fresh reader with a different physical picture in mind.

But I have a question: in your paper arxiv:0811.4416, you write down a "non-relativistic QED" Hamiltonian in eq(54) where the V interaction term involves a sum over electric field modes E_{k,\lambda} up to a "k_max = m_e c/hbar". So apparently, you're imposing a cutoff. But in similar expressions later, including your "trial relativistic Hamiltonian of the Novel QED" eq(60), and the following paragraph, you don't explicitly state the upper limit of the sum over k. Is the upper limit infinity, or are you still imposing a cutoff like k_max?

In the exact relativistic Hamiltonian there is no cutoff. All photon frequencies contribute. The trick is that in the exact relativistic approach there also contributions from "negative frequency" solution components that "cancel" (modify) essentially the high frequency oscillator contributions. This is the exact theory result. In the non-relativistic case this property can be preserved and reasonably reduced to a sum over finite range of photon momenta or frequency.

I have not published the concrete relativistic calculation for many reasons.

Thank you for your discussions, I really appreciate them. I am interested in further discussions. Please, feel free to clarify any subtleties, any motivations, etc.

With best regards,

Bob.

 

[strangerep]

I have not published the concrete relativistic calculation for many reasons.

Thank you for your discussions, I really appreciate them.
I am interested in further discussions.

The details of the full relativistic case are what interests me most, so
probably I won't have much more to say until after you publish that.

 

[Bob_for_short]

The details of the full relativistic case are what interests me most, so probably I won't have much more to say until after you publish that.

Well, thank you anyway. I am glad that I have not heard any conceptual objections from participants.



Bob.

 

[Bob_for_short]

The details of the full relativistic case are what interests me most, so probably I won't have much more to say until after you publish that.

The Novel QED relativistic calculations differ from the standard QED calculations: the interaction Hamiltonian describes a four-fermion potential scattering of compound fermioniums, so the calculation technique is different with naturally taking into account multi-particle electronium structure from the very beginning. It means, for example, inclusive calculations: summation over final states as well as averaging over the initial states since one cannot prepare an electronium in its ground state (in the scattering problems). In bound state description there is averaging over oscillator influence, etc. This is a separate subject and it deserves a separate introduction and treatment.

Regards,

Bob.

 

[Bob_for_short]

For copying-and-pasting:

π²³ ∞ 0° ~ µ ρ σ ∑ Ω √ ∫ ≤ ≥ ± ∃ … ⋅ θ φ ψ ω Ω α β γ δ ∂ ∆ ∇ ε λ Λ Γ ô

 

[Bob_for_short]

The journal version of Atom as a "dressed" nucleus is available for downloading on the journal site:

http://www.springerlink.com/content/h3414375681x8635/?p=b6ac9bb20eec4660b4ea85da36095830&pi=0

 

[Bob_for_short]

The article "On Perturbation Theory for the Sturm-Liouville Problem with Variable Coefficients" by Vladimir Kalitvianski is available at http://arxiv.org/abs/0906.3504.

Here I show how one can reformulate the original problem in order to eliminate big (or divergent) perturbative corrections and obtain finite series from the very beginning.