Pith. sign in

REVIEW 3 major objections 5 minor 1 cited by

Dirac fermions under imaginary rotation

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Free Dirac fermions under imaginary rotation behave, in the thermodynamic limit, like a stationary gas with inverse temperature $q\beta$ when the dimensionless rotation parameter is the irreducible fraction $p/q$.

desk verdict A careful, self-contained derivation of fractal imaginary-rotation thermodynamics for fermions; the core result holds up, but the flux divergence is an order-of-limits artifact that needs a caveat. read the letter →

arxiv 2502.09738 v2 pith:TJ27LMAP submitted 2025-02-13 hep-th nucl-th

Tudor Pătuleanu , Amalia Dariana Fodor , Victor E. Ambrus , Cosmin Crucean This is my paper · ORCID
classification hep-thnucl-th
keywords imaginaryrotationDiracfermionsfractalthermodynamicsvorticaleffectsthermodynamiclimitchemicalpotentialaxialfluxthermalfieldtheory
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper studies a free Dirac fermion gas at finite temperature and chemical potential undergoing rigid rotation with imaginary angular velocity $\Omega = i\Omega_I$. Its central claim is that in the infinite-volume limit the state is indistinguishable, for local observables, from a stationary gas with inverse temperature $\beta_q = q\beta$ and the same chemical potential $\mu$, where $q$ is the denominator of the irreducible fraction $\nu = \beta\Omega_I / 2\pi = p/q$. Because tiny changes in $\nu$ can change $q$ drastically, the effective temperature becomes a fractal, Thomae-like function of the rotation parameter. The paper also shows that the grand potential and thermodynamic functions inherit this fractal behavior, and that the axial and helical fluxes through the transverse plane diverge when $\nu = 1/q$ with $q \to \infty$. The result matters because analytic continuation from imaginary to real rotation, the standard way to interpret rotating plasmas, fails once these fractal asymptotes are reached.

What carries the argument

The machinery is the mode-sum representation of thermal expectation values in cylindrical coordinates, combined with the expansion of the Fermi-Dirac factor into exponential series split by the sign of the effective energy. The rotation enters through the factor $e^{iv\beta\Omega_I m_j}$, and the summation over the half-integer angular momentum $m_j$ is converted into Bessel functions via the summation theorem; for rational $\nu = p/q$ the summation index is written $v = r + qQ$, forcing the trigonometric factors into periodic sequences whose $Q$-sums yield digamma functions. The $q$-dependent constant terms produced by the $r=q$ sector are the fractal asymptotes, while the $r<q$ terms are the transients.

What would settle it

Evaluate the same observables on a cylinder of radius $R$ with explicit boundary conditions (for example, MIT-bag or periodic in the transverse direction) at a rational $\nu = p/q$ and check whether the volume-averaged energy still plateaus at the $T/q$ value as $R$ increases; a plateau that depends on the boundary choice falsifies the universal thermodynamic-limit claim. Alternatively, compute the axial flux by first sending $R\to\infty$ at fixed finite $\nu = 1/q$ and then letting $q\to\infty$; if the flux stays finite, the claimed divergence is an artifact of the limit ordering.

Watch

Extended reading notes

Core claim

The core discovery is that at rational rotation parameter $\nu = p/q$, every finite-temperature observable splits into a coordinate-independent asymptotic piece $A_q$ plus $q-1$ transient pieces that die out with distance from the rotation axis. The asymptotic piece for odd $p+q$ equals the expectation value in a static fermion ensemble at inverse temperature $q\beta$ and the same chemical potential $\mu$; for even $p+q$ the thermal part appears with the opposite sign. The chemical potential terms never fractalize: they enter with the same $\mu$ as the original state, so at large chemical potential the asymptotic energy and charge are dominated by the rotation-blind degenerate contribution $\mu^4/4\pi^2$. In addition, the axial and helical fluxes through a disk of radius $R$ tend, as $R \to \infty$, to finite values that are independent of $\mu$; for $\nu = 1/q$ the axial flux grows linearly in $q$ and diverges as $q \to \infty$, although exactly $\nu = 0$ gives zero flux, exposing a non-commutativity of the limits.

Load-bearing premise

The thermodynamic limit is taken on an open cylinder of radius $R$ with no boundary conditions imposed on the fields; if the infinite-volume limit is sensitive to the boundary prescription or to the order of the $R\to\infty$ and $\nu\to 0$ limits, the fractal asymptotes and the divergent axial flux could be artifacts.

Editorial extensions

If this is right

  • For odd $p+q$, the asymptotic energy, charge, pressure and condensate of the imaginary-rotating gas are exactly those of a static gas at temperature $T/q$ with unchanged chemical potential $\mu$.
  • For even $p+q$, the thermal contributions to the asymptotic quantities appear with the opposite sign, so the state cannot be interpreted as a static equilibrium ensemble.
  • Analytic continuation of imaginary-rotation results to real rotation is reliable only on the principal domain $-1 \le \nu < 1$; the fractal $q$-dependence in the infinite-volume limit makes continuation across periodicity borders impossible.
  • The axial flux through a transverse disk is finite and $\mu$-independent at infinite radius, but diverges as $\nu = 1/q$ with $q \to \infty$, while exactly $\nu = 0$ gives zero, so the limits do not commute.
  • In a dense plasma the asymptotic charge and energy are dominated by the $\mu^4$ terms that do not fractalize, so the fractal signature is most visible at low chemical potential.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension of the paper's calculation is to impose explicit boundary conditions on the cylinder wall and repeat the volume average: the plateau value will show whether the $T/q$ asymptote is universal or an artifact of the open boundary.
  • The same $v = r + qQ$ decomposition should apply to any observable with harmonic angular dependence, so the axial flux's independence of $\mu$ suggests the divergence at $\nu = 1/q$ is controlled by the transverse area rather than by the fermion charge; a similar divergence may occur for a scalar field.
  • The oscillatory transient of the helical flux, whose period scales roughly as $1/(\beta\mu)$, offers a measurable signature that could distinguish the imaginary-rotation regularization in lattice studies before the thermodynamic limit is reached.
  • One could probe the non-commutativity by studying a finite rotating system with small real rotation and checking whether observables develop a plateau at temperature $T/q$ as the system size grows; the paper's result predicts no smooth approach to the zero-rotation limit.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper studies a thermal ensemble of free Dirac fermions with finite inverse temperature β and chemical potential μ, rotating with imaginary angular velocity Ω=iΩ_I. Starting from the mode solutions of the Dirac equation and the thermal field theory formalism, the authors perform the sums over angular momentum and the integrations over momentum to obtain explicit expressions for the fermion condensate, charge currents, helicity and axial currents, energy-momentum tensor components, and the grand-canonical thermodynamic functions. The central result is that for rational rotation parameter ν=βΩ_I/2π=p/q in irreducible form, the large-distance (or large-volume) limit of these observables is governed by a state at effective inverse temperature β_q=qβ with the same chemical potential μ, so that the effective temperature becomes a fractal function of ν. The paper also shows that the chemical-potential terms do not inherit this fractal scaling, computes the transient behavior connecting the on-axis values to the asymptotic values, and evaluates the axial and helical fluxes through a transverse disk, finding in particular that the axial flux for ν=1/q diverges as q→∞. The classical kinetic-theory and real-rotation limits are compared throughout, and the paper emphasizes the failure of analytic continuation from imaginary to real rotation in the thermodynamic limit.

Significance. If the technical construction is accepted, the paper provides a substantial fermionic counterpart to the scalar-field result of Ref. [45], with the new ingredients of chemical potential and chiral/helical currents. The analytical derivation is long, systematic, and internally consistent: key steps include the Fermi-Dirac geometric expansion, summation over angular momentum via the Bessel addition theorem, exact momentum integrations, and reorganization of the v-series for rational ν. The paper is also commendably explicit about its own caveats, including the non-equilibrium nature of the imaginary-rotation state and the non-commutativity of the R→∞ and ν→0 limits. The on-axis results and fractal asymptotes provide concrete predictions that could be compared with lattice or other regularized calculations, and the identification of the helical-flux approach to the axial-flux limit at large chemical potential is an interesting quantitative feature. The main reservations concern the well-posedness of the thermodynamic limit and the scope of the massless restriction.

major comments (3)
  1. [Sec. VIII and Secs. VI–VII] The central thermodynamic-limit claim is not yet well-posed as stated. The paper itself says: 'No boundary conditions were imposed on this cylinder and therefore the thermodynamic system is not well-posed, however this issue disappears when R→∞.' This admission is load-bearing because the fractal asymptotes in Eqs. (202)–(203) are obtained as the R→∞ limit of volume averages whose transient terms, Eqs. (180) and (204), decay only as inverse powers of R, and because the axial-flux divergence in Eq. (215) is a double-limit result: F_A^(1,q)(∞)∝q for ν=1/q→0, whereas strictly ν=0 gives zero. The authors therefore need to define the thermodynamic limit by a specific, boundary-condition-independent prescription (for example, as the limit of a well-posed boundary-value problem with the boundary sent to infinity), and either prove or explicitly renounce the order-of-limits statement needed for each advertised claim. Without such a definition, the equivalence to a static state at β_q=qβ and the divergence of the flux are properties of a particular limiting procedure rather than unique consequences of the QFT calculation.
  2. [Sec. III C, Sec. IV onward, and Abstract] The derivations of the fractal asymptotes, the thermodynamic functions, and the polarization fluxes are all performed in the massless limit M=0, yet the abstract and conclusion state the main result for 'free Dirac fermions' or 'a quantum system of fermions' without this restriction. The massless assumption appears explicitly at the end of Sec. III C, and the treatment of the condensate is via the ratio FC/M as M→0. Since no massive generalization is provided, the title, abstract, and conclusion should either be restricted to massless fermions or supplemented with a statement that the massive case is an open problem; as written, the claimed domain of validity exceeds what is demonstrated.
  3. [Appendix B 2 b and Eqs. (178), (214b), (218b)] For even k=p+q, the series P^r_even is conditionally convergent, and the regularized value is obtained by the symmetrization P^r_even→(P^r_even−P^{q−r}_even)/2. This prescription is a legitimate choice, but it is not obvious that it is the physically unique one. Since the even-k axial and helical flux asymptotes in Eqs. (214b) and (218b) inherit this regularization, the authors should state explicitly that those results are defined by this summation prescription and, ideally, show that other natural resummations (Abel, zeta-function, or a limiting cut-off on Q) lead to the same values. Without this, the even-k flux results are not uniquely determined by the underlying field theory.
minor comments (5)
  1. [Abstract and Sec. V] The wording 'the temperature of the system becomes a fractal function' is stronger than what is proved: the paper establishes a Thomae-like dependence on the denominator q of ν, but no fractal dimension or Hausdorff dimension is computed. Please temper the terminology or add a precise definition of 'fractal' used here.
  2. [Sec. V B and Sec. VI C] The statement that 'the chemical potential breaks the fractalization of fermions' can be misread as meaning that no observable retains fractal behavior at μ≠0. The paper actually shows that the μ-dependent terms do not scale with q while the thermal terms do, so the fractal part remains present but is subdominant at large qβμ. Please clarify this distinction.
  3. [Sec. VIII] There is a typo: 'dissapears' should be 'disappears'.
  4. [Fig. 2 and Fig. 3 captions] The captions contain minor spelling errors: 'rotaion' should be 'rotation' in Fig. 3, and the notation p′/10 is not defined at first use; please define it explicitly when introducing the irreducible fraction p/q.
  5. [Sec. I and Refs. [44,45]] The introduction credits Ref. [44] for the fractal idea and Ref. [45] for the scalar-field calculation, but it would be helpful to state explicitly in the introduction which new physical ingredients (Dirac statistics, chemical potential, chiral/helical currents) are added by the present paper, rather than leaving this to be inferred from the body.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the fractal qβ effective-temperature result and flux divergence are derived from the free-Dirac mode expansion and standard Bessel/polygamma identities, not fitted or assumed.

full rationale

The central claims are obtained by direct evaluation of thermal expectation values of free Dirac fermions. The calculation begins with the density operator ρ=exp[-β(:H-iΩ_I J_z-μQ:)] and the explicit fermionic mode expansion reviewed in Sec. III, expands the Fermi-Dirac factor in Eq. (106), performs the angular-momentum sums using the standard Bessel summation theorem (Eq. (116), from Refs. [54,55]), and integrates the longitudinal and radial modes in Secs. IV D and IV E. The fractal structure arises from the exact split v=r+qQ for rational ν=p/q in Sec. V A, where the r=q terms become coordinate-independent because s_q=sin(pπ)=0. The asymptotic values in Eqs. (176) and (202) follow from elementary zeta-function sums; the identification of these values with a static system at inverse temperature β_q=qβ is made after the calculation, not imposed as an input. The axial-flux divergence in Eq. (215) is an analytic consequence of Eqs. (213)-(214), and the paper explicitly attributes it to the non-commutativity of R→∞ and ν→0, which is a double-limit subtlety rather than a circular step. The admitted statement in Sec. VIII that the cylinder with no boundary conditions is not well-posed is a genuine scientific caveat about the thermodynamic limit, but it does not make the derivation circular. Citations to the authors' earlier work supply mode solutions (Ref. [21]), sesquilinear forms and summation identities (Ref. [7]), and scalar-field integral results (Ref. [45]); these ingredients are restated or standard, and none of them contains the target conclusion. No fitted parameter is renamed as a prediction and no uniqueness theorem is imported to force the choice of β_q. The derivation is therefore self-contained in the sense relevant to circularity.

Assumptions & free parameters 0 free parameters · 6 assumptions · 0 invented entities

No free parameters are fitted: beta, mu and Omega_I are physical inputs. The axioms are standard QFT machinery plus a regularization prescription for conditionally convergent series. No new entities are postulated.

assumptions (6)
  • domain assumption The thermal state is described by the grand canonical density operator rho = exp(-beta(:H - mu Q - i Omega_I J_z:)).
    Defines the quantum state under imaginary rotation; stated in Eq. (66) as the standard extension of the real-rotation density operator.
  • domain assumption The angular momentum spectrum is discrete with half-integer m_j, leading to periodicity nu -> nu+2.
    Follows from the mode solutions in cylindrical coordinates with single-valuedness; used throughout Sec. V to reorganize the series.
  • standard math The Bessel summation theorem (DLMF 10.23.7) can be applied to sum over angular momentum.
    Used in Eq. (116) to obtain Eqs. (114); this is the foundation of the closed-form expressions for the observables.
  • standard math The geometric expansion of the Fermi-Dirac factor is valid for Re(x)>0 and Re(x)<0, and the v=0 'degenerate' term is isolated.
    Eqs. (103)-(106); the degenerate term is essential for the chemical-potential behavior in the asymptotic state.
  • ad hoc to paper For even k=p+q, the conditionally convergent series P^r_even is regularized by symmetrization over r and q-r.
    Appendix B 2 b introduces this prescription because the series diverges logarithmically; the paper notes the special care required.
  • domain assumption The thermodynamic limit is taken as the cylinder radius R -> infinity with no boundary conditions, assuming the ill-posedness disappears.
    The paper explicitly flags this in Sec. VI and the Conclusion, stating that the thermodynamic system is not well-posed without boundary conditions but that the issue disappears as R -> infinity.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Dirac fermions under imaginary rotation." pith.science (2026). https://pith.science/paper/TJ27LMAP

@misc{pith2026250209738,
  author       = {Pith},
  title        = {Pith review of: Dirac fermions under imaginary rotation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TJ27LMAP}},
  note         = {Machine review of arXiv:2502.09738}
}
abstract

In the present study, we investigate the properties of an ensemble of free Dirac fermions, at finite inverse temperature $\beta$ and finite chemical potential $\mu$, undergoing rigid rotation with an imaginary angular velocity $\Omega=i\Omega_I$. Our purpose is to establish the analytical structure of such states, as well as the prospects (and dangers) of extrapolating results obtained under imaginary rotation to the case of real rotation. We show that in the thermodynamic limit, the state of the system is akin to a stationary system with modified inverse temperature $\beta_q = q\beta$ and the same chemical potential, where $q$ is the denominator of the irreducible fraction $\nu = \beta \Omega_I / 2\pi = p/q$. The temperature of the system becomes a fractal function of the rotation parameter, as in the case of the scalar field. The chemical potential breaks the fractalization of fermions. We also compute the thermodynamic potential $\Phi$ and associated thermodynamic functions, showing that they also exhibit fractal behavior. Finally, we evaluate the axial and helical fluxes through the transverse plane, generated through the vortical effects, and show that they diverge in the thermodynamic limit, in the case when $\nu = 1/q$ and $q \to \infty$.

Figures

Figures reproduced from arXiv: 2502.09738 by the authors.

Figure 1
Figure 1. FIG. 1. Thermal expectation values for the observables [PITH_FULL_IMAGE:figures/full_fig_p015_1.png] view at source ↗
Figure 2
Figure 2. shows how the fermion condensate (panel a) and Ttt (panel b) transition from their values on the ro￾tation axis, which are consistent with an analytic con￾tinuation to the case of real rotation, towards their frac￾tal asymptotes, given in Eqs. (176) and indicated with the horizontal black lines (the dashed and solid curves indicate positive and negative asymptotic values, respec￾tively). We now turn to the evaluatio… view at source ↗
Figure 3
Figure 3. FIG. 3. The average energy [PITH_FULL_IMAGE:figures/full_fig_p022_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The average fermion condensate [PITH_FULL_IMAGE:figures/full_fig_p024_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Polarization fluxes through a disk of dimensionless radius [PITH_FULL_IMAGE:figures/full_fig_p025_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. The large- [PITH_FULL_IMAGE:figures/full_fig_p026_6.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Thermodynamics of rotating fermions

    hep-th 2025-09 conditional novelty 5.0 of 10

    A local pressure for rotating massless fermions is proposed that satisfies both the Euler relation and the thermodynamic differential relations, resolving a known spin-hydrodynamics tension.

Reference graph

Works this paper leans on

59 extracted references · 21 canonical work pages · cited by 1 Pith paper

  1. [45]

    Singha, V

    P. Singha, V. E. Ambrus, and M. N. Chernodub, Inhi- bition of the splitting of the chiral and deconfinement transition due to rotation in QCD: The phase diagram of the linear sigma model coupled to Polyakov loops, Phys. Rev. D110, 094053 (2024), arXiv:2407.07828 [hep-ph]

    arXiv 2024

  2. [1]

    Therefore, only the term withσ ′ = 1 will change sign under the absolute value, since|X σ′=1 v |=−X σ′=1 v and sgn(X σ′=1 v ) =−1 whenx < vβ|µ|. Putting the above into practice, we arrive at I±(αv) = 1 2 Z vβ|µ| 0 dx(∓ex−vβ|µ| +e −x−vβ|µ| )eiαvx + cosh(vβµ) Z ∞ vβ|µ| dx e−x+iαvx,(139a) J±(αv) = σµ 2 Z vβ|µ| 0 dx(∓ex−vβ|µ| −e −x−vβ|µ| )eiαvx + sinh(vβµ) Z ...

    work page

  3. [2]

    srµ xr Q+ r q (Q+ r q )2 +x 2r # ,(171a) J z H;r,Q =− iσµ ρq2β2 d dxr

    The QFT results in Eqs. (149) display corrections proportional toν 2 andν 4 that significantly change the expectation values of all observables, asνranges over its domain of periodicity, as shown in Fig. 1. G. Large temperature expansion The expectation valuesA=A deg.+∆A, with ∆Agiven in Eq. (134) in terms of the termsA v, can be obtained in the limit of ...

    work page 2023

  4. [3]

    Oddk=p+q In the case whenk=p+qis odd, Eq

    TheQ r k calculation a. Oddk=p+q In the case whenk=p+qis odd, Eq. (177a) becomes Qr odd(xr) = ∞X Q=0 (−1)Q (Q+ r q )2 +x 2r .(B1) To compute the above series, we employ Eq. (5.7.7) of Ref. [54], given below: ψ z+ 1 2 −ψ z 2 = 2 ∞X k=0 (−1)k k+z .(B2) To arrive at Eq. (B1), we substitutez= r q +ix r and z= r q −ix r in the above relation and take the diffe...

    work page

  5. [4]

    Oddk=p+q In the case whenkis odd, Eq

    TheP r k calculation a. Oddk=p+q In the case whenkis odd, Eq. (178) reduces to P r odd = ∞X Q=0 (−1)Q(Q+ r q ) (Q+ r q )2 +x 2r .(B7) Starting from Eq. (B2), settingz= r q +ix r andz= r q −ix r and adding the results, we arrive at ∆ψr + ∆ψ∗ r = 4P r odd.(B8) Dividing by 4 establishes the third relation in Eq. (178). b. Evenk=p+q In the case whenkis even, ...

    work page

  6. [5]

    Banerjee, J

    N. Banerjee, J. Bhattacharya, S. Bhattacharyya, S. Dutta, R. Loganayagam, and P. Surowka, Hydro- dynamics from charged black branes, JHEP01, 094, arXiv:0809.2596 [hep-th]

    arXiv

  7. [6]

    Erdmenger, M

    J. Erdmenger, M. Haack, M. Kaminski, and A. Yarom, Fluid dynamics of R-charged black holes, JHEP01, 055, arXiv:0809.2488 [hep-th]

    arXiv

  8. [7]

    Torabian and H.-U

    M. Torabian and H.-U. Yee, Holographic nonlinear hy- drodynamics from AdS/CFT with multiple/non-Abelian symmetries, JHEP08, 020, arXiv:0903.4894 [hep-th]

    arXiv

Show all 59 references
  1. [8]

    D. T. Son and P. Surowka, Hydrodynamics with Tri- angle Anomalies, Phys. Rev. Lett.103, 191601 (2009), arXiv:0906.5044 [hep-th]

    2009 arXiv

  2. [9]

    D. E. Kharzeev, J. Liao, S. A. Voloshin, and G. Wang, Chiral magnetic and vortical effects in high-energy nu- clear collisions—A status report, Prog. Part. Nucl. Phys. 88, 1 (2016), arXiv:1511.04050 [hep-ph]

    2016 arXiv

  3. [10]

    V. E. Ambrus and M. N. Chernodub, Vortical effects in Dirac fluids with vector, chiral and helical charges, Eur. Phys. J. C83, 111 (2023), arXiv:1912.11034 [hep-th]

    2023 arXiv

  4. [11]

    V. E. Ambrus, Helical massive fermions under rotation, JHEP08, 016, arXiv:1912.09977 [nucl-th]

    1912 arXiv

  5. [12]

    Landsteiner, E

    K. Landsteiner, E. Megias, and F. Pena-Benitez, Gravi- tational Anomaly and Transport, Phys. Rev. Lett.107, 021601 (2011), arXiv:1103.5006 [hep-ph]

    2011 arXiv

  6. [13]

    Landsteiner, E

    K. Landsteiner, E. Megias, and F. Pena-Benitez, Anoma- lous Transport from Kubo Formulae, Lect. Notes Phys. 871, 433 (2013), arXiv:1207.5808 [hep-th]

    2013 arXiv

  7. [14]

    Vilenkin, Parity Nonconservation and Rotating Black Holes, Phys

    A. Vilenkin, Parity Nonconservation and Rotating Black Holes, Phys. Rev. Lett.41, 1575 (1978)

    1978

  8. [15]

    Vilenkin, MACROSCOPIC PARITY VIOLATING EFFECTS: NEUTRINO FLUXES FROM ROTATING BLACK HOLES AND IN ROTATING THERMAL RA- DIATION, Phys

    A. Vilenkin, MACROSCOPIC PARITY VIOLATING EFFECTS: NEUTRINO FLUXES FROM ROTATING BLACK HOLES AND IN ROTATING THERMAL RA- DIATION, Phys. Rev. D20, 1807 (1979)

    1979

  9. [16]

    Vilenkin, QUANTUM FIELD THEORY AT FINITE TEMPERATURE IN A ROTATING SYSTEM, Phys

    A. Vilenkin, QUANTUM FIELD THEORY AT FINITE TEMPERATURE IN A ROTATING SYSTEM, Phys. Rev. D21, 2260 (1980)

    1980

  10. [17]

    Adamczyket al.(STAR), Global Λ hyperon polariza- tion in nuclear collisions: evidence for the most vortical fluid, Nature548, 62 (2017), arXiv:1701.06657 [nucl-ex]

    L. Adamczyket al.(STAR), Global Λ hyperon polariza- tion in nuclear collisions: evidence for the most vortical fluid, Nature548, 62 (2017), arXiv:1701.06657 [nucl-ex]

    2017 arXiv

  11. [18]

    Adamet al.(STAR), Global polarization of Λ hyperons in Au+Au collisions at √sN N= 200 GeV, Phys

    J. Adamet al.(STAR), Global polarization of Λ hyperons in Au+Au collisions at √sN N= 200 GeV, Phys. Rev. C 98, 014910 (2018), arXiv:1805.04400 [nucl-ex]

    2018 arXiv

  12. [19]

    M. I. Abdulhamidet al.(STAR), Global polariza- tion of Λ and Λ¯hyperons in Au+Au collisions at sNN=19.6 and 27 GeV, Phys. Rev. C108, 014910 (2023), arXiv:2305.08705 [nucl-ex]

    2023 arXiv

  13. [20]

    Adamet al.(STAR), Polarization of Λ ( ¯Λ) hyper- ons along the beam direction in Au+Au collisions at√sN N= 200 GeV, Phys

    J. Adamet al.(STAR), Polarization of Λ ( ¯Λ) hyper- ons along the beam direction in Au+Au collisions at√sN N= 200 GeV, Phys. Rev. Lett.123, 132301 (2019), arXiv:1905.11917 [nucl-ex]

    2019

  14. [21]

    Karpenko and F

    I. Karpenko and F. Becattini, Study of Λ polarization in relativistic nuclear collisions at √sNN = 7.7 –200 GeV, Eur. Phys. J. C77, 213 (2017), arXiv:1610.04717 [nucl- th]

    2017 arXiv

  15. [22]

    Becattini and M

    F. Becattini and M. A. Lisa, Polarization and Vorticity in the Quark–Gluon Plasma, Ann. Rev. Nucl. Part. Sci. 70, 395 (2020), arXiv:2003.03640 [nucl-ex]

    2020 arXiv

  16. [23]

    Becattini, M

    F. Becattini, M. Buzzegoli, G. Inghirami, I. Karpenko, and A. Palermo, Local Polarization and Isothermal Local Equilibrium in Relativistic Heavy Ion Collisions, Phys. Rev. Lett.127, 272302 (2021), arXiv:2103.14621 [nucl- th]

    2021 arXiv

  17. [24]

    B. Fu, S. Y. F. Liu, L. Pang, H. Song, and Y. Yin, Shear- Induced Spin Polarization in Heavy-Ion Collisions, Phys. Rev. Lett.127, 142301 (2021), arXiv:2103.10403 [hep- ph]

    2021 arXiv

  18. [25]

    V. E. Ambru¸ s and E. Winstanley, Rotating quantum states, Phys. Lett. B734, 296 (2014), arXiv:1401.6388 [hep-th]

    2014 arXiv

  19. [26]

    Becattini and E

    F. Becattini and E. Grossi, Quantum corrections to the stress-energy tensor in thermodynamic equilibrium with acceleration, Phys. Rev. D92, 045037 (2015), arXiv:1505.07760 [gr-qc]

    2015 arXiv

  20. [27]

    G. Y. Prokhorov, O. V. Teryaev, and V. I. Zakharov, Unruh effect for fermions from the Zubarev density oper- ator, Phys. Rev. D99, 071901 (2019), arXiv:1903.09697 [hep-th]

    2019 arXiv

  21. [28]

    Becattini, M

    F. Becattini, M. Buzzegoli, and A. Palermo, Exact equi- librium distributions in statistical quantum field theory with rotation and acceleration: scalar field, JHEP02, 101, arXiv:2007.08249 [hep-th]

    2007 arXiv

  22. [29]

    Palermo, M

    A. Palermo, M. Buzzegoli, and F. Becattini, Exact equi- librium distributions in statistical quantum field theory with rotation and acceleration: Dirac field, JHEP10, 077, arXiv:2106.08340 [hep-th]

    arXiv

  23. [30]

    Flachi and K

    A. Flachi and K. Fukushima, Chiral Mass-Gap in Curved Space, Phys. Rev. Lett.113, 091102 (2014), arXiv:1406.6548 [hep-th]

    2014 arXiv

  24. [31]

    Flachi and K

    A. Flachi and K. Fukushima, Chiral vortical effect with finite rotation, temperature, and curvature, Phys. Rev. D98, 096011 (2018), arXiv:1702.04753 [hep-th]

    2018 arXiv

  25. [32]

    V. E. Ambrus and E. Winstanley, Vortical Effects for Free Fermions on Anti-De Sitter Space-Time, Symmetry 13, 2019 (2021), arXiv:2107.06928 [hep-th]

    2021 arXiv

  26. [33]

    Kovtun and A

    P. Kovtun and A. Shukla, Kubo formulas for ther- modynamic transport coefficients, JHEP10, 007, arXiv:1806.05774 [hep-th]

    arXiv

  27. [34]

    A. Jain, P. Kovtun, A. Ritz, and A. Shukla, Hydrody- namic effective field theory and the analyticity of hydro- static correlators, JHEP02, 200, arXiv:2011.03691 [hep- th]

    2011 arXiv

  28. [35]

    Yamamoto and Y

    A. Yamamoto and Y. Hirono, Lattice QCD in ro- tating frames, Phys. Rev. Lett.111, 081601 (2013), arXiv:1303.6292 [hep-lat]

    2013 arXiv

  29. [36]

    V. V. Braguta, A. Y. Kotov, D. D. Kuznedelev, and A. A. Roenko, Influence of relativistic rotation on the confinement-deconfinement transition in gluodynamics, Phys. Rev. D103, 094515 (2021), arXiv:2102.05084 [hep- lat]. 31

    2021 arXiv

  30. [37]

    S. Chen, K. Fukushima, and Y. Shimada, Perturbative Confinement in Thermal Yang-Mills Theories Induced by Imaginary Angular Velocity, Phys. Rev. Lett.129, 242002 (2022), arXiv:2207.12665 [hep-ph]

    2022 arXiv

  31. [38]

    M. N. Chernodub, V. A. Goy, and A. V. Molochkov, In- homogeneity of a rotating gluon plasma and the Tolman- Ehrenfest law in imaginary time: Lattice results for fast imaginary rotation, Phys. Rev. D107, 114502 (2023), arXiv:2209.15534 [hep-lat]

    2023 arXiv

  32. [39]

    V. V. Braguta, M. N. Chernodub, A. A. Roenko, and D. A. Sychev, Negative moment of inertia and rotational instability of gluon plasma, Phys. Lett. B852, 138604 (2024), arXiv:2303.03147 [hep-lat]

    2024 arXiv

  33. [40]

    Azuma and T

    T. Azuma and T. Morita, A Scaling Relation, Zm-Type Deconfinement Phases, and Imaginary Chemical Poten- tials in Finite Temperature Large-N Gauge Theories, PTEP2024, 093B03 (2024), arXiv:2406.10672 [hep-th]

    2024

  34. [41]

    Jiang and J

    Y. Jiang and J. Liao, Pairing Phase Transitions of Matter under Rotation, Phys. Rev. Lett.117, 192302 (2016), arXiv:1606.03808 [hep-ph]

    2016 arXiv

  35. [42]

    M. N. Chernodub and S. Gongyo, Effects of rotation and boundaries on chiral symmetry breaking of rel- ativistic fermions, Phys. Rev. D95, 096006 (2017), arXiv:1702.08266 [hep-th]

    2017 arXiv

  36. [43]

    M. N. Chernodub, Inhomogeneous confining-deconfining phases in rotating plasmas, Phys. Rev. D103, 054027 (2021), arXiv:2012.04924 [hep-ph]

    2021 arXiv

  37. [44]

    F. Sun, K. Xu, and M. Huang, Splitting of chiral and de- confinement phase transitions induced by rotation, Phys. Rev. D108, 096007 (2023), arXiv:2307.14402 [hep-ph]

    2023 arXiv

  38. [46]

    S. Chen, K. Fukushima, and Y. Shimada, Inhomogeneous confinement and chiral symmetry breaking induced by imaginary angular velocity, Phys. Lett. B859, 139107 (2024), arXiv:2404.00965 [hep-ph]

    2024 arXiv

  39. [47]

    Jiang, Rotating SU(2) gluon matter and deconfine- ment at finite temperature, Phys

    Y. Jiang, Rotating SU(2) gluon matter and deconfine- ment at finite temperature, Phys. Lett. B853, 138655 (2024), arXiv:2312.06166 [hep-th]

    2024 arXiv

  40. [48]

    M. N. Chernodub, Fractal thermodynamics and ninionic statistics of coherent rotational states: realization via imaginary angular rotation in imaginary time formalism, (2022), arXiv:2210.05651 [quant-ph]

    2022 arXiv

  41. [49]

    V. E. Ambru¸ s and M. N. Chernodub, Rigidly rotat- ing scalar fields: Between real divergence and imagi- nary fractalization, Phys. Rev. D108, 085016 (2023), arXiv:2304.05998 [hep-th]

    2023 arXiv

  42. [50]

    S. R. de Groot, W. A. van Leeuwen, and C. G. van Weert, Relativistic kinetic theory: Principles and applications (North-Holland Publ. Comp, Amsterdam, 1980)

    1980

  43. [51]

    Cercignani and G

    C. Cercignani and G. M. Kremer,The Relativistic Boltz- mann Equation: Theory and Applications(Springer, 2002)

    2002

  44. [52]

    Rezzolla and O

    L. Rezzolla and O. Zanotti,Relativistic Hydrodynam- ics(Oxford University Press, Oxford, United Kingdom, 2013)

    2013

  45. [53]

    Tolman and P

    R. Tolman and P. Ehrenfest, Temperature Equilibrium in a Static Gravitational Field, Phys. Rev.36, 1791 (1930)

    1930

  46. [54]

    R. C. Tolman, On the Weight of Heat and Thermal Equi- librium in General Relativity, Phys. Rev.35, 904 (1930)

    1930

  47. [55]

    V. E. Ambrus , and E. Winstanley, Exact solutions in quantum field theory under rotation, inStrongly Inter- acting Matter under Rotation, edited by F. Becattini, J. Liao, and M. Lisa (Springer International Publishing, Cham, 2021) pp. 95–135, arXiv:1908.10244 [hep-th]

    2021 arXiv

  48. [56]

    S. L. Adler, Axial vector vertex in spinor electrodynam- ics, Phys. Rev.177, 2426 (1969)

    1969

  49. [57]

    J. S. Bell and R. Jackiw, A PCAC puzzle:π 0 →γγin theσmodel, Nuovo Cim. A60, 47 (1969)

    1969

  50. [58]

    F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark,NIST handbook of mathematical functions(Cam- bridge University Press, New York, NY, 2010)

    2010

  51. [59]

    I. S. Gradshteyn and I. M. Ryzhik,Table of integrals, series, and products, eighth edition ed. (Academic Press, 2015)

    2015

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.