RELATIVISTIC INVARIANCE OF THE VACUUM

Before publishing in The European Physical Journal C, my result underwent long peer-review, with several rejections. Here I present excerpts from the reports, with comments. Thanks to all referees the novelty of my proof is now much better supported. If you are interested in full correspondence, it is available on request by email: abednorz[at]fuw.edu.pl.

1. Physical Review D (rejected after 4 rounds and 2 stages of appeal)

Referee A (Editor Rashmi Ray):
"In this paper the author analyzes the Lorentz invariance of the zero-temperature Green's functions in Quantum Field Theory, using the so called Closed Time Path formalsm. I cannot see in the paper new physical results that could warrant publication in the Physical Review D. Lorentz. The proof of Lorentz invariance seems to be contained in subsections IV C and IV D. Section IV C deals with free propagators, no use of CTP formalism. Section IV D includes interactions. Which would be the difference working with the standard in-out formalism? In any case, the fact that there is a preferred time coordinate is already present in canonical quantization, where it is well known that it does not spoil Lorentz invariance. Finally, along the paper the author describes finite temperature field theory, and acknowledges the fact that at non vanishing temperature the theory is not Lorentz invariant. I do not see any justification for including the description of the case T≠ 0. For these reasons, I consider that the paper is not suitable for publication"

Comment: The referee writes "not new" but does not give any reference.

Referee B (Editor Rashmi Ray) :
PDF of the report

Comment: Only this referee tried to show a "simple proof", based on the book Thermal Field Theory by Michel Le Bellac, Cambridge Univ. Press, 1996 (Referee may be Le Bellac himself or his close colleague). His\her "proof" relies on the fact that invariance has been already shown for each flat part separately (I agree) and can be extended to all of them by a vertical shift σ which decouples flat parts when going to infinity (see figure below). He/she assumes that the averages do not depend on the shift. It is true only if energies/frequencies of particles sum up to zero independently for each flat part. In general only the total sum of energies/frequencies is zero, not for single flat parts, and the the amplitude depends of the shift. Hence, the "simple proof" is wrong (or at least not so general as mine).



Referee C (Editor Rashmi Ray):
"I do not really understand what the authors are trying to show. If the field is in an equilibrium state (e g., the true vacuum) then by definition the CTP integral cannot give anything different than other methods (e. g. canonical ones), so a new proof of Lorentz invariance is not required. If it is not in equilibrium, it is to be expected that the same means that brought it out of equilibrium (e.g., preparation or explicit interaction with an environment) will break Lorentz invariance. In other words, I find the two reports already at hand rather convincing, it is very unlikely that I would reach a different conclusion."

Comment:
Again, like referee A, this referee claims "not new" but does not give any reference. He/she refers to "canonical methods" but what does it mean? Canonical quantization? So how to set up a proof out of this?

Referee D (Editor Rashmi Ray):
"The author studies the Lorentz symmetry of the vacuum Green functions of quantum fields in the closed time path (CTP) formulation of QFT. He presents a proof that the latter have the correct symmetry property directly based the path integral formulation on the closed time contour. I have analyzed in detail the proof presented in the paper as well as the criticisms of the three previous referees and the corresponding answers by the author. I agree with the authors that the paper definitely presents new material and his proof of Lorentz invariance is new. However, I also share the view of the previous referees that the obtained result is not new (see below) and thus the paper does not really add anything to the question apart from presenting things in a novel way, directly using CTP formulation. I believe this, however, is of interest to only a very specialized readership and does not warrant publication in Physical Review D. Consider first the two-point Green function of a real scalar field. The latter has in principle four CTP components. However, in general only two of them are independent (e.g. the statistical and the spectral two-point functions). For systems at finite temperature or in the vacuum, the fluctuation-dissipation relation reduces this further to only one component. The latter can be chosen as the one having both argument on the upper branch of the CTP, i.e., the Feynman propagator. For the later, Lorentz covariance can be shown by standard proofs (e.g., based on the in-out path integral formalism). One concludes that standard proofs are enough to prove the Lorentz covariance of the CTP propagator. The argument generalizes to the two-point function of any kind of (complex scalar, fermionic, etc.) field. The number of independent CTP components of higher n-point functions increases with n and it is not clear that one can again reduce the discussion to the case where all time arguments lie on the upper branch. So the previous argument may not apply. However, standard proofs demonstrate that all in-out n-point functions have the correct symmetry property under Lorentz transformations, which is sufficient to show that both the dynamics and the vacuum of the theory are Lorentz invariant. This is enough to guarantee that all the correlation functions of the theory (including those which cannot be written as in-out Green's function, e.g., those which are not a time-ordered product of field operators) are Lorentz covariant. This includes the various components of CTP Green functions. I conclude that the present proof, although it is interesting in its own right, does not add anything new there.

Comment:
The referee claims that in-out functions are sufficient to show that the vacuum is invariant. How?

Editorial Board Member V.P. Nair (Editor Dennis Nordstrom):
I have read through the entire paper and the comments by the reviewers and the author's responses. My evaluation is as follows. First of all, I think this paper is unnecessarily long, with a lot of material which is more or less well-known and standard. The real essence of the paper is in Sec IV.C and Sec IV.D. The main result which is claimed is the Lorentz invariance of the theory (QED) as the temperature goes to zero within the closed-time-path formalism. I shall consider a number of points to help arrive at a fair evaluation. Let me start with the question of whether the result is new. The result that we have Lorentz invariance as β → ∞ is not new. This paper presents a proof entirely within the specific context of the CTP formalism, and there is something here which has not been published anywhere, something new in that sense, although arguments do exist within the CTP formalism for Lorentz invariance. So if the proof calls for important extensions of concepts or leads to significantly more general results, then there is a good rationale for publication. What is proved is, first, the Lorentz invariance of the scalar propagator (as β → ∞) and then this is argued to lead to the desired result for all n-point functions within perturbation theory, essentially because the n-point functions have an expansion in terms of propagators and vertices. The interaction Lagrangian is taken to be Lorentz invariant, so, the invariance of the propagator generalizes in a completely straightforward manner to the n-point functions. It is important to keep in mind that this argument, as some of the alternate arguments presented by the referees, works because the Green's functions have an analytic continuation into the complex time-domain. The question we may now ask is: How does this compare with other proofs of Lorentz invariance, so we can gauge whether there is something substantially new? The "simple proof" referred to by the referee B is not entirely in the CTP formalism, as the author has pointed out, but given that one needs to take for granted that the Green's functions can be analytically continued to the complex time-domain, I do not see this as a serious handicap of the "simple proof". Nevertheless, it is true that the "simple proof" is not obtained entirely within the CTP formalism. The arguments presented by the referee D are the clearest in this regard. Proof of Lorentz invariance in the CTP formalism can be obtained by relating various two-point functions (via analyticity arguments) to the corresponding Feynman propagator. The argument does extend, at least within perturbation theory (which is all the author is showing here as well) to n-point functions. The field theory is ultimately defined by the n-point functions, so one does have a proof of Lorentz invariance. In this regard, I disagree with the reply comment of the author to the point made by the referee D to the effect that the n-point functions do not suffice. In summary, yes, there is a small amount of material here which may be considered new. But it is not a new result per se; even within the CTP formalism it is more like an alternate proof, as the arguments presented by the referee D constitute another (and already existing) proof. On these grounds, I would not recommend publication in the Physical Review D.

Comment:
By analyticity? The argument does extend? How? Since I could find email of V.P. Nair I contacted him and asked for more clarifications. He refused, so I claim V.P. Nair lies in his report.

APS Editor-in-Chief Gene D. Sprouse (Editor Dennis Nordstrom):
"Dear Dr. Bednorz, I have reviewed the file concerning this manuscript which was submitted to Physical Review D15. The scientific review of your paper is the responsibility of the editor of Physical Review D15 which resulted in the decision to reject your paper. The Editor-in-Chief must assure that the procedures of our journals have been followed responsibly and fairly in arriving at that decision. On considering all aspects of this file I have concluded that our procedures have in fact been appropriately followed and that your paper received a fair review. Accordingly, I must uphold the decision of the Editors."

Comment:
So Editor-in-Chief accepts a lie in the report of the Editorial Board Member V.P. Nair. Conclusion: editors/referees can openly lie in reports and the journal policy accepts it. It is an unacceptable abuse to science. By the the way the message of Editor-in-Chief is automatic, I have found an identical rejection of another manuscript from 2005. All rejected manuscripts probably recieve the same message.

2. Journal of High Energy Physics (rejected after single round and appeal).

First Report:
"The paper is not sufficiently interesting to deserve publication. The motivations are rather weak. In particular the perturbative proof of the Lorentz invariance of the S-matrix implies that the representation of the asymptotic (free) fields is defined by a Lorentz invariant vacuum, which, by general results, coincides with the vacuum of the representation of the interacting fields. Moreover the presentation is excessively detailed and long for a rather limited problem."

Comment:
By general results? I demand a reference!

Second Report (appeal):
"This paper does not present results which are interesting enough to warrant a publication in JHEP."

Comment:
So now it is only not interesting. All the relativity is not interesting nor the vacuum?

3. New Journal of Physics (rejected without review).

Editorial Board Member (Editors Kryssa Roycroft and Joanna Bewley):
"Without really getting very deep into the technical details of the paper, what the author claims he proves here is not a very surprising thing. I am of the opinion that what he claims to have proved was already very well known (let me put it this way: if the result had been the opposite I'd have believed it's probably not correct at first sight). It was new to me what he claims that there is no general proof that the relativistic invariance of the vacuum was not guaranteed by the invariance of the Lagrangian. I would discuss it is proved and that adding a more general but perturbative proof doesn't really add that much knowledge to the problem. His proof is of interest no doubt, and if it's correct it may add some interesting technical details backing up what I believe was already well-known. But in my opinion it is indeed rather incremental for NJP. The problem he claims to have solved is definitely not an open question in field theory. At least not from the point of view of people who do physics (maybe mathematicians would like it better) . This said, I do think it's publishable (if correct), not in NJP, though. I would recommend, if we are not to leave IOP, to submit to the journal of Physics A, whose audience is more suited to the kind of question he addresses and the techniques he presents. "

Comment:
So it is enough to believe. I haven't supposed that NJP prefers religion to science. In real science such facts like invariance of the vacuum must be proved, not just "believed".

4. The European Journal of Physics C (accepted after a single round).

The referee agreed with the novelty of my proof, its importance and the criticism of "simple proofs". Thanks!