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REVIEW 2 major objections 5 minor 2 cited by

Adiabatic subtraction yields finite, covariant stress-tensor components for charged scalar QED in dS3 with an electric field: E²/m strong-field growth, and no Weyl anomaly in the massless conformal limit.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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2026-08-03 17:02 UTC pith:PSXMM6PF

load-bearing objection A genuinely new dS3 scalar QED EMT computation, but the headline strong-field scaling looks like a subtraction-scheme artifact and the prose overclaims it as Schwinger physics. the 2 major comments →

arxiv 2512.10864 v3 pith:PSXMM6PF submitted 2025-12-11 hep-th

Induced energy-momentum tensor of the scalar field in 3D de Sitter QED

Manizheh Botshekananfard , Takahiro Hayashinaka This is my paper
classification hep-th
keywords induced energy-momentum tensoradiabatic regularizationde Sitter spacetimeSchwinger effectvacuum polarizationtrace anomalyscalar QEDthree dimensions
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper seeks to supply the missing explicit renormalized energy-momentum tensor for a charged scalar field in three-dimensional de Sitter spacetime with a uniform electric field. Using adiabatic subtraction on in-vacuum Whittaker modes, it obtains finite, covariant expressions for all components of the induced tensor. The central results are the asymptotics: in strong electric fields the energy density grows as E²/m, a vacuum-polarization effect rather than direct pair production, while in the infrared the components diverge as 1/m. In the massless, conformally coupled limit the trace vanishes, matching the expectation that odd-dimensional spacetimes have no genuine Weyl anomaly. The value is a concrete, covariant backreaction tensor where none existed, plus a sharp check of odd-dimensional trace behavior.

Core claim

On the paper's own terms, the claim is that after subtracting second-order adiabatic counterterms from the in-vacuum expectation values, the renormalized components (4.16)-(4.18) are finite and covariantly conserved. In the strong-field limit they obey T00 = -T11 = T22 approximately (Omega^2 H^3 / 4 pi^2)(-pi lambda^2/(12 lambda_m)), so the induced energy density is quadratic in the electric field and inversely proportional to mass; in the infrared, T00 approximately (Omega^2 H^3 / 4 pi^2)(-17/32 - pi lambda^2/(12 lambda_m)) with similar 1/m corrections in the spatial components. In the ordered massless conformal limit, the trace of the tensor vanishes, which the paper reads as confirmation

What carries the argument

The machinery is the mode decomposition of the charged scalar in the Poincaré patch of dS3 in terms of Whittaker functions (special solutions of the radial mode equation), together with adiabatic regularization: a WKB expansion of the positive-frequency mode to second adiabatic order produces counterterms that remove the ultraviolet divergences from the mode integrals. The key structural choice is treating the external electric potential as zeroth adiabatic order and truncating at second order; the surviving finite parts, including the terms controlling the strong-field and infrared asymptotics, come from that subtraction plus Mellin-Barnes residue evaluations of the Whittaker integrals.

Load-bearing premise

The physical content of the final tensor is fixed by the paper's state and subtraction choices—in-vacuum Whittaker modes, electric potential at zeroth adiabatic order, truncation at second order—so if a different renormalization prescription shifts the finite coefficients, the headline E²/m and 1/m asymptotics are not unique predictions.

What would settle it

Compute the same renormalized stress tensor with covariant point-splitting in the same dS3 in-vacuum state and compare the strong-field coefficient of T00 with (5.1). A mismatch would show that the adiabatic scheme, not the physics, sets the strong-field asymptotics.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The finite, covariant expressions provide an explicit renormalized stress tensor for dS3 scalar QED that can be used in semiclassical backreaction studies.
  • In the strong-field limit, the E²/m energy growth is driven by vacuum polarization rather than by the particle-production component, distinguishing the mechanism behind the Schwinger-like scaling.
  • In the infrared, the 1/m divergences show that the exactly massless limit is singular even after ultraviolet regularization, so light scalar fields in dS3 acquire parametrically large vacuum stresses.
  • The vanishing trace in the massless conformally coupled limit provides an explicit consistency check that no genuine Weyl anomaly exists in odd-dimensional spacetimes.
  • The off-diagonal momentum-flux component, nonvanishing before renormalization, vanishes afterward, consistent with symmetric production of positive and negative charges.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The strong-field coefficient in (5.1) is the negative of a finite term in the adiabatic counterterm (4.12), so its value is tied to the subtraction scheme; an independent point-splitting calculation in the same state would reveal which part of the E²/m scaling is physical.
  • The vanishing trace is obtained under a specific order of limits (lambda to 0 before xi to 1/8 and lambda_m to 0); reversing the order could leave a finite remainder, which the paper would classify as scheme-dependent, and this is directly checkable from (6.1).
  • The 1/m infrared divergence suggests that a fully massless dS3 scalar QED requires an infrared completion, such as a mass resummation or a stochastic formalism, which the paper does not supply.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 5 minor

Summary. The paper computes the renormalized expectation value of the energy-momentum tensor (EMT) for a charged scalar field in three-dimensional de Sitter spacetime in the presence of a uniform electric field, using adiabatic regularization. The authors obtain explicit finite expressions for the EMT components (4.16)-(4.18), study their strong-field and infrared limits, and examine the trace. The central claims are: (i) the strong-field limit behaves as T00 = -T11 = T22 ≈ (Ω²H³/4π²)(-πλ²/(12λm)) [Eq. (5.1)]; (ii) the infrared limit is given by (5.2)-(5.4); (iii) the trace vanishes in the massless, conformally coupled limit [Eq. (6.2)], consistent with the absence of a Weyl anomaly in odd dimensions. The paper presents a long, explicit computation with integral representations in Appendix A and states that these are the first explicit renormalized EMT expressions for dS3 scalar QED.

Significance. If the computation is correct, this would be a useful first explicit result for vacuum polarization in three-dimensional de Sitter QED, providing a benchmark for backreaction studies and a consistency check for the absence of a trace anomaly in odd dimensions. The manuscript is self-contained, with a detailed mode decomposition, residue evaluations, and an explicit trace check. The adiabatic regularization setup is clearly stated. However, the physical interpretation of the strong-field and trace results is weakened by the scheme dependence of the finite counterterm remainder and by an improperly specified limiting procedure. These issues bear directly on the paper's headline conclusions, so the manuscript requires revision before the claims can be accepted as stated.

major comments (2)
  1. [§5.1, Eq. (5.1) and §4, Eqs. (4.12)-(4.14)] The leading strong-field term in Eq. (5.1), proportional to λ²/λm, is exactly the finite, cutoff-independent piece of the second-order adiabatic counterterm. In Eq. (4.12), the counterterm T00^(2) contains +π/12 λ²/λm, and after subtraction (4.16) retains -π/12 λ²/λm; the same pattern holds for T11 and T22. Since the other terms in (4.16)-(4.18) contain no 1/λm factor, the 1/m dependence of the claimed asymptotic behavior is entirely inherited from the subtraction scheme. The choice Aμ = O(adiabatic order 0) and the truncation at second order are not uniquely fixed by UV divergence subtraction. The paper therefore needs to impose an independent renormalization condition (e.g., matching a flat-space limit or requiring a reference-vacuum condition) or explicitly state that the coefficient in (5.1) is scheme-dependent and not a parameter-free prediction. As written, the abstract and conclus
  2. [§6, Eq. (6.2)] The trace limit is written as an iterated limit: lim_{λ→0} lim_{ξ→1/8} lim_{λm→0} T = 0. But Eq. (6.1) contains the term -π/12 λ²/λm, which diverges as λm→0 for any fixed nonzero λ. If the limits are evaluated in the order indicated, the result is divergent, not zero. To check the conformal massless trace, one must either set λ=0 before taking λm→0, or specify a simultaneous limit with λ²/λm→0. The paper does not provide such a specification, so the claimed verification of the vanishing trace is not demonstrated as stated. This is a load-bearing consistency check, and the manuscript should be corrected to define the limit unambiguously.
minor comments (5)
  1. [§5, first paragraph] The text states that in the strong-field limit the induced quantities show 'exponential enhancement,' but Eq. (5.1) is an algebraic power law (λ²). This contradicts the paper's own asymptotics and should be corrected.
  2. [§5.2] The sentence 'the energy–momentum tensor diverges as λm^{-1} ∝ m^{-2}' is incorrect: λm = m/H, so λm^{-1} ∝ m^{-1}, not m^{-2}. The neighboring text correctly says m^{-1}.
  3. [§7, Conclusion] The conclusion says that in the infrared regime the induced quantities are 'exponentially suppressed,' but the IR expansions (5.2)-(5.4) contain a constant term and a λ²/λm term, not an exponential. This overstates the IR behavior and should be revised.
  4. [Eq. (5.1)] The chain T00 = -T11 = T22 is ambiguous. It should be written as T00 ≈ -T11 ≈ T22 ≈ (Ω²H³/4π²)(-πλ²/(12λm)) or with explicit signs for each component, to avoid confusion about the sign pattern.
  5. [Acknowledgments] The paragraph containing a corporate disclaimer is unusual for a journal submission and should be removed unless required by the authors' institutions; it is not standard scientific content.

Circularity Check

0 steps flagged

No circular derivation; strong-field coefficient is scheme-dependent but explicitly acknowledged and not a self-citation artifact.

full rationale

The derivation chain is self-contained: the Whittaker mode functions are standard solutions, the bare EMT is computed directly from the mode expansion in Sec. 3, the adiabatic WKB counterterms are derived from the same Klein-Gordon equation in Sec. 4, and the renormalized components (4.16)-(4.18) are the difference with cutoff terms cancelled. The vanishing trace in the massless conformal limit, Eq. (6.2), is an external consistency check, not an input. The only potentially concerning point is that the strong-field leading term, Eq. (5.1), is the negative of a finite term in the second-order adiabatic counterterm, Eq. (4.12): T00 = -T11 = T22 ~ (Omega^2 H^3/4pi^2)(-pi lambda^2/(12 lambda_m)). This makes the coefficient convention-dependent through the choice that A_mu is zeroth adiabatic order and the truncation at second order. That is a renormalization-scheme ambiguity rather than circularity, and the paper explicitly acknowledges such residues as 'scheme-dependent renormalization artifact[s]' (Sec. 6) and 'state-dependent rather than geometrical' (Sec. 7). No fitted parameter is renamed as a prediction, no uniqueness theorem is imported from the authors' prior work, and self-citations are contextual rather than load-bearing. Thus no circular step meets the quoted-reduction standard.

Axiom & Free-Parameter Ledger

0 free parameters · 6 axioms · 0 invented entities

The computation adds no fitted numbers and no invented entities: physical inputs are m, E, H, and ξ, scanned over parameter ranges in the figures; the UV cutoff Λ cancels between bare and counterterm expressions. The load-bearing inputs are: (1) the in-vacuum state defined by the Whittaker modes (Eq. 2.20); (2) the adiabatic scheme — Aμ at zeroth adiabatic order, counterterms truncated at second order (§4) — whose finite parts set the strong-field coefficient in Eq. (5.1); (3) the test-field approximation (§2); (4) validity of the Mellin-Barnes representation (Eq. 2.16) at imaginary γ; (5) the unshown residue evaluations (A.8)-(A.14); (6) the odd-dimensional no-anomaly theorem as the external benchmark for §6.

axioms (6)
  • domain assumption The in-vacuum state defined by the Whittaker modes (2.14)-(2.15) is the physical vacuum for the computation.
    All expectation values are evaluated in this state (Eq. 2.20); a different state choice would change the finite parts of the renormalized tensor.
  • domain assumption Adiabatic regularization with Aμ at zeroth adiabatic order and counterterms truncated at second adiabatic order.
    The finite remainder of the renormalized tensor depends on this scheme; the leading strong-field term (5.1) coincides with the finite counterterm piece in (4.12). §4.
  • domain assumption The electromagnetic and gravitational fields are classical backgrounds unaffected by the scalar field (test-field approximation).
    Stated at the start of §2; no backreaction on the metric or gauge field is included.
  • standard math Mellin-Barnes representation (2.17) and its analytic continuation remain valid for the parameter ranges used, including imaginary γ in the strong-field regime.
    Conditions (2.16) are stated, but their enforcement at γ→iλ (λ≫1) is not demonstrated.
  • ad hoc to paper The residue evaluations (A.8)-(A.14) are correct.
    The appendix states 'applying the theorem of residues, eventually we have' with no derivation shown; these integrals feed directly into all final expressions.
  • standard math Absence of genuine Weyl (trace) anomaly in odd-dimensional spacetimes.
    Used in §6 as the external expectation against which Eq. (6.2) is checked; cited to [1,2,16].

pith-pipeline@v1.3.0-alltime-deepseek · 4660 in / 4829 out tokens · 273000 ms · 2026-08-03T17:02:06.797083+00:00 · methodology

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read the original abstract

In this work, we derive the renormalized expectation value of the energy--momentum tensor of a quantized charged scalar field in three-dimensional de Sitter spacetime $\mathrm{dS}_{3}$ in the presence of a uniform electric field. Using the adiabatic regularization method, ultraviolet divergences are systematically removed, yielding finite expressions for all components of the induced tensor. We analyze the behavior of the renormalized energy--momentum tensor in both the strong-field and infrared regimes. In the strong-field limit, the induced energy density exhibits a quadratic dependence on the electric field strength; however, this leading contribution is dominated by vacuum polarization effects rather than directly by the Bogoliubov particle-production component. In the infrared regime, the tensor shows a pronounced inverse-mass dependence, indicating strong infrared sensitivity characteristic of light scalar fields in de Sitter spacetime. In the conformally coupled massless limit, the renormalized trace vanishes, as expected from the absence of a genuine Weyl anomaly in odd-dimensional spacetimes. These results provide a precise characterization of vacuum polarization and infrared effects in three-dimensional de Sitter scalar QED.

discussion (0)

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Forward citations

Cited by 2 Pith papers

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

  1. Massless fermionic current of Schwinger pairs in 3D de Sitter spacetime

    hep-th 2026-07 reject novelty 7.0

    Massless fermions in dS_3 with a constant electric field produce a finite monotonic induced current: linear in E for weak fields, λ^{3/2} for strong fields.

  2. Massless fermionic current of Schwinger pairs in 3D de Sitter spacetime

    hep-th 2026-07 accept novelty 6.0

    Massless fermions in dS3 produce a finite, monotonic induced current linear at weak electric fields and semiclassical at strong fields, with no infrared hyperconductivity.

Reference graph

Works this paper leans on

64 extracted references · 3 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Birrell and P.C.W

    N.D. Birrell and P.C.W. Davies, Quantum Fields in Curved Space , Cambridge University Press, Cambridge, UK (1982)

    1982

  2. [2]

    Parker and D.J

    L. Parker and D.J. Toms, Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity, Cambridge University Press, Cambridge, UK (2009)

    2009

  3. [3]

    Wald, Quantum Field Theory in Curved Spacetime and Black Hole Ther modynamics, University of Chicago Press, Chicago (1994)

    R.M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Ther modynamics, University of Chicago Press, Chicago (1994)

    1994

  4. [4]

    Parker, Quantized fields and particle creation in expanding univers es

    L. Parker, Quantized fields and particle creation in expanding univers es. i , Phys. Rev. 183 (1969) 1057

    1969

  5. [5]

    Parker, Quantized fields and particle creation in expanding univers es

    L. Parker, Quantized fields and particle creation in expanding univers es. ii , Phys. Rev. D 3 (1971) 346

    1971

  6. [6]

    Hawking, Zeta function regularization of path integrals in curved sp acetime, Communications in Mathematical Physics 55 (1977) 133

    S.W. Hawking, Zeta function regularization of path integrals in curved sp acetime, Communications in Mathematical Physics 55 (1977) 133

    1977

  7. [7]

    Parker and S.A

    L. Parker and S.A. Fulling, Adiabatic regularization of the energy-momentum tensor of a quantized field in homogeneous spaces , Phys. Rev. D 9 (1974) 341

    1974

  8. [8]

    Birrell, The application of adiabatic regularization to calculatio ns of cosmological interest , Proceedings of the Royal Society of London

    N. Birrell, The application of adiabatic regularization to calculatio ns of cosmological interest , Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 361 (1978) 513

    1978

  9. [9]

    Bunch and P.C

    T.S. Bunch and P.C. Davies, Quantum field theory in de sitter space: renormalization by point-splitting, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences 360 (1978) 117

    1978

  10. [10]

    Anderson and L

    P.R. Anderson and L. Parker, Adiabatic regularization in closed robertson-walker univ erses, Phys. Rev. D 36 (1987) 2963

    1987

  11. [11]

    Habib, C

    S. Habib, C. Molina-Par ´ ıs and E. Mottola, Energy-momentum tensor of particles created in an expanding universe , Phys. Rev. D 61 (1999) 024010

    1999

  12. [12]

    Anderson, W.A

    P.R. Anderson, W.A. Hiscock and D.A. Samuel, Stress-energy tensor of quantized scalar fields in static spherically symmetric spacetimes , Phys. Rev. D 51 (1995) 4337

    1995

  13. [13]

    Anderson and E

    P.R. Anderson and E. Mottola, Quantum vacuum instability of “eternal” de sitter space , Phys. Rev. D 89 (2014) 104039

    2014

  14. [14]

    Christensen, Vacuum expectation value of the stress tensor in an arbitrar y curved background: The covariant point-separation method , Phys

    S.M. Christensen, Vacuum expectation value of the stress tensor in an arbitrar y curved background: The covariant point-separation method , Phys. Rev. D 14 (1976) 2490 . – 21 –

    1976

  15. [15]

    Christensen, Regularization, renormalization, and covariant geodesic point separation, Phys

    S.M. Christensen, Regularization, renormalization, and covariant geodesic point separation, Phys. Rev. D 17 (1978) 946

    1978

  16. [16]

    Wald, Trace anomaly of a conformally invariant quantum field in cur ved spacetime, Phys

    R.M. Wald, Trace anomaly of a conformally invariant quantum field in cur ved spacetime, Phys. Rev. D 17 (1978) 1477

    1978

  17. [17]

    Bunch, Adiabatic regularisation for scalar fields with arbitrary c oupling to the scalar curvature, Journal of Physics A: Mathematical and General 13 (1980) 1297

    T. Bunch, Adiabatic regularisation for scalar fields with arbitrary c oupling to the scalar curvature, Journal of Physics A: Mathematical and General 13 (1980) 1297

    1980

  18. [18]

    Strominger, The ds/cft correspondence , Journal of High Energy Physics 2001 (2001) 034

    A. Strominger, The ds/cft correspondence , Journal of High Energy Physics 2001 (2001) 034

    2001

  19. [19]

    Gibbons and S.W

    G.W. Gibbons and S.W. Hawking, Cosmological event horizons, thermodynamics, and particl e creation, Phys. Rev. D 15 (1977) 2738

    1977

  20. [20]

    Mottola, Particle creation in de sitter space , Phys

    E. Mottola, Particle creation in de sitter space , Phys. Rev. D 31 (1985) 754

    1985

  21. [21]

    Markkanen, A

    T. Markkanen, A. Rajantie, S. Stopyra and T. Tenkanen, Scalar correlation functions in de sitter space from the stochastic spectral expansion , Journal of Cosmology and Astroparticle Physics 2019 (2019) 001

    2019

  22. [22]

    La Sapienza

    J. Sol` a, Running vacuum in the universe: current phenomenological s tatus, in The Fourteenth Marcel Grossmann Meeting On Recent Developments in Theoret ical and Experimental General Relativity, Astrophysics, and Relativistic Field Theorie s: Proceedings of the MG14 Meeting on General Relativity, University of Rome “La Sapienza”, Ital y, 12–18 July 2015 ...

    2015

  23. [23]

    Deser, R

    S. Deser, R. Jackiw and G. Hooft, Three-dimensional einstein gravity: dynamics of flat space , Annals of Physics 152 (1984) 220

    1984

  24. [24]

    Witten, 2+ 1 dimensional gravity as an exactly soluble system , Nuclear Physics B 311 (1988) 46

    E. Witten, 2+ 1 dimensional gravity as an exactly soluble system , Nuclear Physics B 311 (1988) 46

    1988

  25. [25]

    Polyakov, De sitter space and eternity , Nuclear physics B 797 (2008) 199

    A. Polyakov, De sitter space and eternity , Nuclear physics B 797 (2008) 199

    2008

  26. [26]

    Bavarsad, C

    E. Bavarsad, C. Stahl and S.-S. Xue, Scalar current of created pairs by schwinger mechanism in de sitter spacetime , Phys. Rev. D 94 (2016) 104011

    2016

  27. [27]

    Unruh, Experimental black-hole evaporation? , Physical Review Letters 46 (1981) 1351

    W.G. Unruh, Experimental black-hole evaporation? , Physical Review Letters 46 (1981) 1351

    1981

  28. [28]

    Visser, Acoustic black holes: horizons, ergospheres and hawking ra diation, Classical and Quantum Gravity 15 (1998) 1767

    M. Visser, Acoustic black holes: horizons, ergospheres and hawking ra diation, Classical and Quantum Gravity 15 (1998) 1767

    1998

  29. [29]

    Barcelo, S

    C. Barcelo, S. Liberati and M. Visser, Analogue gravity, Living reviews in relativity 14 (2011) 3

    2011

  30. [30]

    Weinfurtner, E.W

    S. Weinfurtner, E.W. Tedford, M.C. Penrice, W.G. Unruh and G.A. Lawrence, Measurement of stimulated hawking emission in an analogue system , Physical review letters 106 (2011) 021302

    2011

  31. [31]

    Steinhauer, Observation of quantum hawking radiation and its entanglem ent in an analogue black hole , Nature Physics 12 (2016) 959

    J. Steinhauer, Observation of quantum hawking radiation and its entanglem ent in an analogue black hole , Nature Physics 12 (2016) 959

    2016

  32. [32]

    Garriga, Pair production by an electric field in (1+1)-dimensional de sitter space, Phys

    J. Garriga, Pair production by an electric field in (1+1)-dimensional de sitter space, Phys. Rev. D 49 (1994) 6343

    1994

  33. [33]

    Fillion-Gourdeau and S

    F. Fillion-Gourdeau and S. MacLean, Time-dependent pair creation and the schwinger mechanism in graphene , Physical Review B 92 (2015) 035401

    2015

  34. [34]

    Schmitt, P

    A. Schmitt, P. Vallet, D. Mele, M. Rosticher, T. Taniguchi, K. Wat anabe et al., Mesoscopic klein-schwinger effect in graphene , Nature Physics 19 (2023) 830

    2023

  35. [35]

    Nation, J.R

    P.D. Nation, J.R. Johansson, M.P. Blencowe and F. Nori, Colloquium: Stimulating uncertainty: Amplifying the quantum vacuum with superconducting circui ts, Reviews of Modern Physics 84 (2012) 1

    2012

  36. [36]

    Volovik, The universe in a helium droplet , vol

    G.E. Volovik, The universe in a helium droplet , vol. 117, OUP Oxford (2003). – 22 –

    2003

  37. [37]

    Deser, R

    S. Deser, R. Jackiw and S. Templeton, Three-dimensional massive gauge theories , Phys. Rev. Lett. 48 (1982) 975

    1982

  38. [38]

    Schwinger, On gauge invariance and vacuum polarization , Phys

    J. Schwinger, On gauge invariance and vacuum polarization , Phys. Rev. 82 (1951) 664

    1951

  39. [39]

    Heisenberg and H

    W. Heisenberg and H. Euler, Consequences of dirac theory of the positron , arXiv preprint physics/0605038 (2006)

    Pith/arXiv arXiv 2006

  40. [40]

    Sauter, ¨Uber das verhalten eines elektrons im homogenen elektrisch en feld nach der relativistischen theorie diracs , Zeitschrift f¨ ur Physik69 (1931) 742

    F. Sauter, ¨Uber das verhalten eines elektrons im homogenen elektrisch en feld nach der relativistischen theorie diracs , Zeitschrift f¨ ur Physik69 (1931) 742

    1931

  41. [41]

    Gelis and N

    F. Gelis and N. Tanji, Schwinger mechanism revisited , Progress in Particle and Nuclear Physics 87 (2016) 1

    2016

  42. [42]

    G.V. Dunne, Heisenberg–euler effective lagrangians: basics and extens ions, in From Fields to Strings: Circumnavigating Theoretical Physics: Ian Kogan Memorial Collection (In 3 Volumes), pp. 445–522, World Scientific (2005)

    2005

  43. [43]

    Bavarsad, S.P

    E. Bavarsad, S.P. Kim, C. Stahl and S.-S. Xue, Effect of a magnetic field on schwinger mechanism in de sitter spacetime , Phys. Rev. D 97 (2018) 025017

    2018

  44. [44]

    creation of spin 1/2 particles by an electric field in de sitter space

    S. Haouat and R. Chekireb, Comment on “creation of spin 1/2 particles by an electric field in de sitter space” , Phys. Rev. D 87 (2013) 088501

    2013

  45. [45]

    La Sapienza

    C. Stahl, E. Strobel and S.-S. Xue, Pair creation in the early universe , in The Fourteenth Marcel Grossmann Meeting On Recent Developments in Theoret ical and Experimental General Relativity, Astrophysics, and Relativistic Field Theorie s: Proceedings of the MG14 Meeting on General Relativity, University of Rome “La Sapienza”, Ital y, 12–18 July 2015 , p...

    2015

  46. [46]

    Haouat and R

    S. Haouat and R. Chekireb, Effect of the electric field on the creation of fermions in de-s itter space-time, arXiv preprint arXiv:1504.08201 (2015)

    Pith/arXiv arXiv 2015

  47. [47]

    Hayashinaka, T

    T. Hayashinaka, T. Fujita and J. Yokoyama, Fermionic schwinger effect and induced current in de sitter space , Journal of Cosmology and Astroparticle Physics 2016 (2016) 010

    2016

  48. [48]

    Stahl, E

    C. Stahl, E. Strobel and S.-S. Xue, Fermionic current and schwinger effect in de sitter spacetime, Phys. Rev. D 93 (2016) 025004

    2016

  49. [49]

    Hayashinaka and J

    T. Hayashinaka and J. Yokoyama, Point splitting renormalization of schwinger induced curr ent in de sitter spacetime , Journal of Cosmology and Astroparticle Physics 2016 (2016) 012

    2016

  50. [50]

    Hayashinaka and S.-S

    T. Hayashinaka and S.-S. Xue, Physical renormalization condition for de sitter qed , Phys. Rev. D 97 (2018) 105010

    2018

  51. [51]

    Akbari Ahmadmahmoudi and E

    M. Akbari Ahmadmahmoudi and E. Bavarsad, Energy-momentum tensor and effective lagrangian of scalar qed with a nonminimal coupling in 2d de s itter spacetime, Phys. Rev. D 103 (2021) 105009

    2021

  52. [52]

    Gholizadeh Meimanat and E

    O. Gholizadeh Meimanat and E. Bavarsad, Induced energy-momentum tensor in de sitter scalar qed and its implication for induced currents , Phys. Rev. D 107 (2023) 125001

    2023

  53. [53]

    Botshekananfard and E

    M. Botshekananfard and E. Bavarsad, Induced energy-momentum tensor of a dirac field in 2d de sitter qed , Phys. Rev. D 101 (2020) 085011

    2020

  54. [54]

    Stahl and S.-S

    C. Stahl and S.-S. Xue, Schwinger effect and backreaction in de sitter spacetime , Physics Letters B 760 (2016) 288

    2016

  55. [55]

    Turner and L.M

    M.S. Turner and L.M. Widrow, Inflation-produced, large-scale magnetic fields , Phys. Rev. D 37 (1988) 2743

    1988

  56. [56]

    El-Menoufi, Inflationary magnetogenesis and non-local actions: The con formal anomaly , Journal of Cosmology and Astroparticle Physics 2016 (2016) 055

    B.K. El-Menoufi, Inflationary magnetogenesis and non-local actions: The con formal anomaly , Journal of Cosmology and Astroparticle Physics 2016 (2016) 055. – 23 –

    2016

  57. [57]

    Moreno-Pulido and J

    C. Moreno-Pulido and J. Sol` a Peracaula, Running vacuum in quantum field theory in curved spacetime: renormalizing the vacuum energy density withou t ∼m4 terms, The European Physical Journal C 80 (2020) 1

    2020

  58. [58]

    Kim, Schwinger effect, hawking radiation and unruh effect , International Journal of Modern Physics D 25 (2016) 1645005

    S.P. Kim, Schwinger effect, hawking radiation and unruh effect , International Journal of Modern Physics D 25 (2016) 1645005

    2016

  59. [59]

    Hollands and R.M

    S. Hollands and R.M. Wald, Local wick polynomials and time ordered products of quantum fields in curved spacetime , Communications in Mathematical Physics 223 (2001) 289 [gr-qc/0103074]

    Pith/arXiv arXiv 2001

  60. [60]

    Kim and D.N

    S.P. Kim and D.N. Page, Schwinger pair production in electric and magnetic fields , Physical Review D 73 (2006) 065020

    2006

  61. [61]

    Bavarsad, C

    E. Bavarsad, C. Stahl and S.S. Xue, Scalar pair production in de sitter spacetime , Physical Review D 93 (2016) 105018

    2016

  62. [62]

    Fr¨ ob, J

    M.B. Fr¨ ob, J. Garriga, S. Kanno, M. Sasaki, J. Soda, T. Tanak a et al., Schwinger effect in de sitter space, Journal of Cosmology and Astroparticle Physics 2014 (2014) 009

    2014

  63. [63]

    Fulling and L

    S.A. Fulling and L. Parker, Renormalization in the theory of a quantized scalar field int eracting with a robertson-walker spacetime , Annals of Physics 87 (1974) 176

    1974

  64. [64]

    Kobayashi and N

    T. Kobayashi and N. Afshordi, Schwinger effect in 4d de sitter space and constraints on magnetogenesis in the early universe , Journal of High Energy Physics 2014 (2014) 1. – 24 –

    2014