REVIEW
Photon Quantization and Propagator in Rotating Coordinates
High Energy Physics - Phenomenology · Submitted 2 Oct 2026 · 95 references
Pith's verdict: The vector photon construction is genuinely new and internally consistent, with two cross-checked derivations and limitations the authors state plainly; it deserves referee time despite computing no observable.
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Referee report
The paper
The paper claims
The paper aims to establish that Maxwell theory in Feynman gauge quantizes cleanly in rigidly rotating cylindrical coordinates, yielding two physical photon modes per total angular momentum sector and a gauge-fixed propagator with poles…
The reading
What carries the argument
The load-bearing object is the total rotation generator $\hat{J}_z = \hat{L}_z + \hat{D}_z$, the sum of the orbital angular momentum $\hat{L}_z = -i\partial_\phi$ and the generator $\hat{D}_z$ acting on the transverse circular polarization vectors $\epsilon_\pm$, which carries the field's intrinsic spin contribution. Because the covariant vector Laplacian acting on the transverse components reads $(\partial_t - i\Omega\hat{J}_z)^2 - \nabla_\perp^2 - \partial_z^2$ plus a mixing term, modes of definite $j$ combine Bessel functions of orders $j-1$, $j$, and $j+1$, and the two independent solutions are fixed by the reduced Lorenz condition. A second, alternative construction generates the same modes by multiplying scalar eigenfunctions by the covariantly constant tetrad, $\Psi^\mu_a = e^\mu_a\,u_j$; both routes feed the Maxwell inner product that fixes the normalization and the canonical commutation relations, and both routes into the propagator, the tensor-transformed scalar Green function and the Fock–Schwinger spectral sum, reproduce the same gauge-fixed two-point function.
Extended reading notes
Core claim
The central claim is that Maxwell theory in Feynman gauge, written covariantly in rigidly rotating cylindrical coordinates, admits a complete set of physical photon modes organized by the total angular momentum $j = l \pm 1$, and that quantizing on these modes yields a photon propagator whose spectral poles sit at $E_l = |q| - l\Omega$. The vector structure forces a distinction between the orbital generator $\hat{L}_z$ and the intrinsic transverse-rotation generator $\hat{D}_z$; the two independent physical polarizations per sector are selected by imposing the reduced Lorenz condition after using the residual gauge freedom to remove the temporal component. The paper constructs the same full gauge-fixed propagator in two independent ways, from the scalar Green function transformed as a bitensor and from the covariant vector eigensystem built on a covariantly constant tetrad via spectral decomposition and the Fock–Schwinger proper-time representation, and verifies that both satisfy $\nabla_\beta\nabla^\beta D^{\mu\nu}(x,x') = -i\,g^{\mu\nu}(x)\,\delta^4(x-x')$.
Load-bearing premise
The whole construction rests on taking the transverse plane to be unbounded with continuous transverse momentum and no radial boundary condition, so the propagators are local Green functions valid inside the light cylinder $\Omega\rho<1$ rather than normal-mode Green functions of a finite rotating cylinder.
Editorial extensions
If this is right
- Covariant perturbative QED in a rotating medium now has an internal photon-line propagator, with the complete gauge-fixed Maxwell operator inverted in rotating coordinates.
- Internal photon lines acquire the rotational energy shift $E_l = |q| - l\Omega$ at their spectral poles, so any loop or photon-mediated observable computed in the rotating frame will carry an angular-momentum-dependent energy structure.
- In the rigid-rotation approximation $\Omega(t-t') + (\phi-\phi') = 0$, the gauge-fixed propagator factorizes into the free Minkowski scalar propagator times a coordinate-dependent bitensor $g^{\mu\nu}(x,x')$, reducing the rotation to a geometric tensor factor.
- The physical and gauge-fixed propagators are distinct objects: the former serves correlation functions of physical photon states, while only the latter may be used as the internal photon propagator in covariant perturbation theory.
Reading between the lines
- If the construction is correct, the same mode basis should extend to finite temperature and finite density, since the formalism organizes photon states by angular momentum rather than by a translationally invariant vacuum.
- Imposing Fourier–Bessel boundary conditions at a finite cylinder radius $R$ with $\Omega R < 1$ would turn the delta-normalized modes into discrete-normalized modes and would produce the normal-mode photon propagator the authors deliberately leave unbuilt.
- Comparing the photon pole shift with the fermionic propagators of the rotating-medium literature would test whether quantization on the total angular momentum generalizes the known dispersion pattern from spin-1/2 to spin-1.
- The most direct application would be a dilepton or photon-production calculation in a rotating thermal medium using this gauge-fixed propagator, benchmarked against the rigid-rotation approximation results already published.
Original abstract
We construct the quantized electromagnetic field and the corresponding photon propagators in a rigidly rotating cylindrical reference frame. Starting from covariant Maxwell theory, we formulate the gauge-fixed field equations and solve them in cylindrical coordinates. The vector nature of the electromagnetic field requires distinguishing orbital and intrinsic angular momentum, with the total angular momentum as the natural quantum number. We construct the two independent physical photon modes in terms of Bessel functions by solving the coupled differential equations, and provide an alternative construction based on a covariant basis of vector eigenfunctions generated by a covariantly constant tetrad. After normalizing the modes with the Maxwell inner product, we quantize the electromagnetic field and define the corresponding photon states and greater and lesser two-point functions. The physical time-ordered propagator is obtained directly from the quantized modes, with its transverse dependence encoded in polarization kernels that retain the cylindrical spatial structure and its spectral poles exhibiting the rotational energy shift. The full gauge-fixed photon propagator is constructed in two complementary ways: from the scalar Green function combined with the tensor transformation of the inertial Feynman-gauge propagator, and from the covariant vector eigensystem through its spectral decomposition and the Fock--Schwinger proper-time representation. We verify that both constructions satisfy the Green-function equation for the complete gauge-fixed Maxwell operator, providing the propagator required for covariant perturbative calculations with internal photon lines.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
We construct the quantized electromagnetic field and the corresponding photon propagators in a rigidly rotating cylindrical reference frame. Starting from covariant Maxwell theory, we formulate the gauge-fixed field equations and solve them in cylindrical coordinates. The vector nature of the electromagnetic field requires distinguishing orbital and intrinsic angular momentum, with the total angular momentum as the natural quantum number. We construct the two independent physical photon modes in terms of Bessel functions by solving the coupled differential equations, and provide an alternative construction based on a covariant basis of vector eigenfunctions generated by a covariantly constant tetrad. After normalizing the modes with the Maxwell inner product, we quantize the electromagnetic field and define the corresponding photon states and greater and lesser two-point functions. The physical time-ordered propagator is obtained directly from the quantized modes, with its transverse dependence encoded in polarization kernels that retain the cylindrical spatial structure and its spectral poles exhibiting the rotational energy shift. The full gauge-fixed photon propagator is constructed in two complementary ways: from the scalar Green function combined with the tensor transformation of the inertial Feynman-gauge propagator, and from the covariant vector eigensystem through its spectral decomposition and the Fock--Schwinger proper-time representation. We verify that both constructions satisfy the Green-function equation for the complete gauge-fixed Maxwell operator, providing the propagator required for covariant perturbative calculations with internal photon lines.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We construct the quantized electromagnetic field and the corresponding photon propagators in a rigidly rotating cylindrical reference frame. | contribution 1.00 | 0.96 | 0.19 | asserted 1.00 |
| s1 | Starting from covariant Maxwell theory, we formulate the gauge-fixed field equations and solve them in cylindrical coordinates. | method 0.99 | 0.93 | 0.03 | asserted 1.00 |
| s2 | The vector nature of the electromagnetic field requires distinguishing orbital and intrinsic angular momentum, with the total angular momentum as the natural quantum number. | background 0.66 | 0.34 | 0.06 | asserted 1.00 |
| s3 | We construct the two independent physical photon modes in terms of Bessel functions by solving the coupled differential equations, and provide an alternative construction based on a covariant basis of vector eigenfunctions generated by a covariantly constant tetrad. | method 0.69 | 0.95 | 0.12 | asserted 1.00 |
| s4 | After normalizing the modes with the Maxwell inner product, we quantize the electromagnetic field and define the corresponding photon states and greater and lesser two-point functions. | method 0.86 | 0.95 | 0.08 | asserted 1.00 |
| s5 | The physical time-ordered propagator is obtained directly from the quantized modes, with its transverse dependence encoded in polarization kernels that retain the cylindrical spatial structure and its spectral poles exhibiting the rotational energy shift. | result 0.83 | 0.94 | 0.25 | asserted 1.00 |
| s6 | The full gauge-fixed photon propagator is constructed in two complementary ways: from the scalar Green function combined with the tensor transformation of the inertial Feynman-gauge propagator, and from the covariant vector eigensystem through its spectral decomposition and the Fock--Schwinger proper-time representation. | method 0.75 | 0.94 | 0.17 | asserted 1.00 |
| s7 | We verify that both constructions satisfy the Green-function equation for the complete gauge-fixed Maxwell operator, providing the propagator required for covariant perturbative calculations with internal photon lines. | result 0.70 | 0.94 | 0.36 | asserted 1.00 |
What was examined, and what was not
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References
Discussion
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