Off-Shell Quantum Fields to Connect Dressed Photons with Cosmology
Round 1
Reviewer 1 Report
In the work the authors propose a connection between a type of off-shell quantum fields, dubbed dressed photons, with cosmology. In particular, they argue that a dressed photon, much like as Dark Energy, can be interpreted in terms of spacelike momenta of the electromagnetic field.
The authors start with a detailed review of the dressed photon technology and related quantum field theory aspects. They introduce a novel idea of a Clebsh dual field, make connection with cosmology, and explain how a space-like momentum field is materialized by a Majorana fermion, and finally investigate why the latter is related to phenomena of dressed photons, Dark Matter etc.
Their work is strengthening some kind of interdisciplinary perspective and I think should be published.
Author Response
Thank you so much for spending your precious time in reviewing our manuscript.
Your positive comments are encouraging and highly appreciated.
Reviewer 2 Report
This paper describes an application of the dressd-photon idea, developed
previously by some of the authors, to cosmology. Unfortunately, the paper is
not very clear, and it is not free of derision (as in "serious lack of
imagination").
Moreover, the theoretical part of the paper is not convincing. The discussion
on page 7 aims to show that there is a new degree of freedom of photons which
has been missed by previous well-established and decades-old studies. However,
this putative degree of freedom is not physical because the authors simply do
not impose the required gauge invariance of electrodynamics. (They mention
gauge-fixing terms in their methods section, but omit imposing the
corresponding constraint.) In preceding passages, it seems, they try to argue
that such a degree of freedom might be physical in quantum field theory
because of the possibility of virtual particles. However, while the particle
picture is certainly more general in quantum field theory than in classical
field theories, it must remain gauge invariant. The degree of freedom
described by the authors is a consequence of explicitly broken gauge
invariance (as can be seen by a mass term in equations of motion for the
vector potential), not of virtual particles. The authors seem to be confusing
this physical violation of gauge invariance with the formal introduction of
gauge-fixing terms in certain quantization methods.
On page 8, the authors attempt to link their field description of photons with
gravity, based on a formal analogy between their stress-energy tensor and the
Einstein tensor. This analogy, being merely formal and only briefly elaborated,
remains unconvincing. The observation at the beginning of Section 3,
relating a timelike condition (13) to a description of de Sitter space, also
stays at a very formal level with obscure physics.
The application to cosmology is rather contrived. The authors attempt to
construct a stress-energy tensor that resembles what would be obtained from a
cosmological constant. However, they do not derive this property in any
sense. They rather assume a specific (fine-tuned?) field configuration to
obtain (23). Since this leads to negative energy density, they complexify
their fields and arrive at (26). In spite of their claim in the following
paragraph, this stress-energy tensor still does not resemble what would be
required for a cosmological constant.
Author Response
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Reviewer 3 Report
The manuscript discusses the concept of recently proposed dressed photons, theorized as off-shell massive photons occupying finite spatial volume. Dressed photons are argued to be relevant in understanding the physics of nanoscale systems. The authors have an extensive history of dressed photon research and publications. The manuscript offers interesting proposals for dark matter and dark energy in terms of dressed photon phenomenology. The proposal is quite original. The introduction to the dressed photon concept is well written. The proposed explanations for dark matter and dark energy in terms of dressed photons and broken symmetries are well developed and very interesting to consider. The number and range of references are sufficient. The concepts explored in the manuscript warrant manuscript publication.
Author Response
Thank you so much for spending your precious time in reviewing our manuscript.
Your positive comments are encouraging and highly appreciated.
Reviewer 4 Report
This paper considers the possible connection of the concept of "dressed photons", developed by one of the authors, with cosmology, and in particular, with the dark energy and dark matter problems.
After an introduction on technological implications of dressed photons and a review of the formalism, the paper focuses on the cosmological implications. For that purpose a Robertson-Walker background is considered and the energy-momentum tensor of the Clebsh dual field is computed and related to dark energy.
The paper is interesting, and the connection between cosmology and dressed photons should be further explored, unfortunately the discussion about the possible interpretation of the obtained energy-momentum as dark energy or dark matter has important drawbacks:
1.- The quantity $^*\hat T^\mu_\nu(3)$ is defined for complexified fields rather than for the original $S_{\mu\nu}$ fields. A physical interpretation of those "Hodge dual" fields is missing.
2.- The energy-momentum tensor (26) is not compatible with an homogeneous and isotropic Robertson-Walker background, because of the non-vanishing $T^{0i}$ components. Being dark energy the dominant contribution at late times, this form of the energy-momentum tensor is phenomenologically not viable, unless $\sigma\ll \tau$. However in such a case, the effective equation of state for dark energy would be $p=-\rho/3$, which is unable to drive accelerated expansion and incompatible with Planck data for a constant equation of state.
3.- Even though the metric is assumed to be of the Robertson-Walker form, the calculations performed in section 4 are actually done in Minkowski space-time. In the cosmological context, this approximation is valid only for sub-Hubble scales, and it ignores the scaling behaviour of the mode solutions with the scale factor $R(t)$. As a matter of fact, the sentence "our universe is observationally shown to have a flat spacetime structure" is misleading, as observations only indicate that spatial sections are nearly flat.
4.- The discussion on the possible interpretation as dark matter is not clearly exposed. It is mentioned that is related to the energy of the Weyl tensor, but a proper definition of such energy is not presented. A conclusive proof that the field behaves as a non-relativistic fluid (with vanishing pressure) and weak interactions to the visible sector is not provided.
Author Response
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Round 2
Reviewer 2 Report
The authors have made some changes, but the main issues remain. First, the arguments that non-gauge-invariant quantities may be used to describe physics are unconvincing. In particular, in the methods section the authors use a Lagrangian (29) which implies the correct field equations in Lorentz gauge, but only if the Lorentz gauge condition (\partial_\mu A^\mu=0) is imposed. However, instead of imposing the gauge condition, the authors treat it as a new independent degree of freedom, related to L_\nu in equation (5). There is no physical justification for this treatment of the electromagnetic field.
Secondly, the cosmological claims about dark energy are incompletely justified because the authors compare only the trace of their stress-energy tensor (26) with the phenomenologically viable case of a cosmological constant. However, the complete form of (26) shows that it implies a strong violation of spatial isotropy, which is inconsistent with large-scale cosmological observations. (The matrix in (26) does not have an eigenvalue with multiplicity 3.)
Author Response
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Round 3
Reviewer 2 Report
My comment about Lorentz gauge was made only in the context of the specific equation (29), which is written in Lorentz gauge. I did not imply that the Lorentz gauge is the only possible gauge choice. However, in any gauge, one must impose complete gauge fixing conditions in addition to the equations of motion, and the authors fail to do so when they consider phi in equation (30) as a physical degree of freedom.
Similarly, their treatment of the Nakanishi-Lautrup formalism fails to impose a gauge fixing condition, but for different reasons. The Lorentz gauge can certainly be generalized to the condition written in equation (33). However, one has to deal with the new field B in a proper way. If B is fixed (such as a constant, but this is not necessary), the first equation in (33) indeed fixes the gauge, but B is not dynamical. If B is left free as a dynamical field, as the authors prefer, the first equation in (33) does not fix the gauge. Moreover, B, even with the second equation in (33) imposed, is not gauge invariant because it inherits some gauge transformations from A through the first equation in (33). A consistent formulation therefore requires an additional condition on B to completely fix the gauge. This is why B is not physical but rather represents gauge degrees of freedom. The authors' arguments to use B for physical effects, omitting proper gauge fixing conditions, are unconvincing.
In their cosmological applications, the authors now argue that one should use a 3x3 minor in order to read off spatial pressure components. However, taking a minor is not a Lorentz covariant operation and therefore applies only in one frame. In this frame, there is, in addition to isotropic pressure, also a non-zero energy flow determined by the time-space components of the matrix (23) (unless tau=0 or sigma=0). This energy flow points in a preferred direction in this frame, which implies the same spatial anisotropy that follows from the covariant argument I gave in my previous report,
based on eigenvalues of the matrix (23).
Author Response
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