- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access
  • Access by Xinjiang University

Computational quantum field theory for fermion pair creation in two-dimensional curved spacetimes

Mohammed Alkhateeb1,2, James P. Edwards2, and Yves Caudano1

PDF

Phys. Rev. D 113, 125002 – Published 2 June, 2026

DOI: https://doi.org/10.1103/gb8d-kqc5

Abstract

Similarly to the well-known particle-antiparticle pair production process in strong electromagnetic fields (the Schwinger effect), the matter field vacuum state can be excited by time-dependent, curved spacetime geometries. We study this process using a spacetime resolved numerical approach in the interaction picture by extending computational quantum field theory (CQFT), well-adapted to simulate the time evolution of quantum fields, to spin-1/2 fermions in curved spacetime. Within this framework, we investigate vacuum excitation of a Dirac field induced by a spacetime-curvature quench. In particular, we evolve the fermionic Minkowski vacuum in a 1+1-dimensional idealized curved spacetime characterized by a localized Gaussian deformation of flat spacetime. Particle production is quantified by fermion-antifermion pair numbers defined with respect to the Minkowski basis of asymptotically flat spacetime. We analyze how the excitation depends on the strength and spatial extent of the curvature deformation and discuss the numerical implementation of CQFT in curved backgrounds. While the postquench geometry is static and no electromagnetic field is included, this work establishes a foundation for studying particle creation in genuinely time-dependent curved spacetimes and electromagnetic backgrounds.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (66)

  1. J. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82, 664 (1951).
  2. F. Sauter, Über das verhalten eines elektrons im homogenen elektrischen feld nach der relativistischen theorie Diracs, Z. Phys. 69, 742 (1931).
  3. Werner Heisenberg and Heinrich Euler, Folgerungen aus der diracschen theorie des positrons, Z. Phys. 98, 714 (1936).
  4. V. Weisskopf, Über die Elektrodynamik des Vakuums auf Grund der Quantentheorie des Elektrons,” Kongelige Danske Videnskabernes Selskab, Matematisk-fysiske Meddelelser 14, 1 (1936), https://cds.cern.ch/record/406571.
  5. A. Fedotov, A. Ilderton, F. Karbstein, Ben King, D. Seipt, H. Taya, and Greger Torgrimsson, Advances in QED with intense background fields, Phys. Rep. 1010, 1 (2023).
  6. Jin Woo Yoon, Yeong Gyu Kim, Il Woo Choi, Jae Hee Sung, Hwang Woon Lee, Seong Ku Lee, and Chang Hee Nam, Realization of laser intensity over 1023 w/cm2, Optica 8, 630 (2021).
  7. H. Abramowicz, M. Almanza Soto, M. Altarelli, R. Aßmann, A. Athanassiadis, G. Avoni, T. Behnke, M. Benettoni, Y. Benhammou et al. (LUXE Collaboration), Technical design report for the LUXE experiment, Eur. Phys. J. Special Topics 233, 1709 (2024).
  8. V. Yakimenko, L. Alsberg, E. Bong, G. Bouchard, C. Clarke, C. Emma, S. Green, C. Hast, M. J. Hogan, J. Seabury et al., Facet-ii facility for advanced accelerator experimental tests, Phys. Rev. Accel. Beams 22, 101301 (2019).
  9. S. W. Hawking, Particle creation by black holes, Commun. Math. Phys. 43, 199 (1975).
  10. Stephen A. Fulling, Nonuniqueness of canonical field quantization in Riemannian space-time, Phys. Rev. D 7, 2850 (1973).
  11. P. C. W. Davies, Scalar production in Schwarzschild and Rindler metrics, J. Phys. A 8, 609 (1975).
  12. W. G. Unruh, Notes on black-hole evaporation, Phys. Rev. D 14, 870 (1976).
  13. Y. Rosenberg, Optical analogues of black-hole horizons, Phil. Trans. R. Soc. A 378, 20190232 (2020).
  14. J. Drori, Y. Rosenberg, D. Bermudez, Y. Silberberg, and U. Leonhardt, Observation of stimulated Hawking radiation in an optical analogue, Phys. Rev. Lett. 122, 010404 (2019).
  15. A. Pandey, A note on analogue semi-classical gravity in (1+1) dimensions, Gravitation Cosmol. 30, 229 (2024).
  16. A. Pelat, F. Gautier, S. C. Conlon, and F. Semperlotti, The acoustic black hole: A review of theory and applications, J. Sound Vib. 476, 115316 (2020).
  17. M. M. Roberts and T. Wiseman, Analog gravity and continuum effective theory of the graphene tight-binding lattice model, Phys. Rev. B 109, 045425 (2024).
  18. Yao Wang, Chong Sheng, Yong-Heng Lu, Jun Gao, Yi-Jun Chang, Xiao-Ling Pang, Tian-Huai Yang, Shi-Ning Zhu, Hui Liu, and Xian-Min Jin, Quantum simulation of particle pair creation near the event horizon, Natl. Sci. Rev. 7, 1476 (2020).
  19. T. Cheng, Q. Su, and R. Grobe, Introductory review on quantum field theory with space-time resolution, Contemp. Phys. 51, 315 (2010).
  20. T. Cheng, Q. Su, and R. Grobe, Creation of multiple electron-positron pairs in arbitrary fields, Phys. Rev. A 80, 013410 (2009).
  21. D. D. Su, Y. T. Li, Q. Z. Lv, and J. Zhang, Enhancement of pair creation due to locality in bound-continuum interactions, Phys. Rev. D 101, 054501 (2020).
  22. C. K. Li, Y. J. Li, Q. Su, and R. Grobe, Phase sensitivity of the pair-creation process in colliding laser pulses, Phys. Rev. A 108, 033112 (2023).
  23. M. Alkhateeb, X. Gutiérrez de la Cal, M. Pons, D. Sokolovski, and A. Matzkin, Relativistic time-dependent quantum dynamics across supercritical barriers for Klein-Gordon and Dirac particles, Phys. Rev. A 103, 042203 (2021).
  24. X. Gutiérrez de la Cal, M. Alkhateeb, M. Pons, A. Matzkin, and D. Sokolovski, Klein paradox for bosons, wave packets and negative tunnelling times, Sci. Rep. 10, 19225 (2020).
  25. M. Alkhateeb and A. Matzkin, Space-time-resolved quantum field approach to Klein-tunneling dynamics across a finite barrier, Phys. Rev. A 106, L060202 (2022).
  26. M. Alkhateeb and A. Matzkin, Evolution of strictly localized states in noninteracting quantum field theories with background fields, Phys. Rev. A 109, 062223 (2024).
  27. Mohammed Alkhateeb, X. Gutierrez de la Cal, M. Pons, D. Sokolovski, and A. Matzkin, Relativistic quantum field theory approach to electron wave-packet tunneling: A fully causal process, Phys. Rev. A 111, 012222 (2025).
  28. Antonio Ferreiro, Jose Navarro-Salas, and Silvia Pla, Role of gravity in the pair creation induced by electric fields, Phys. Rev. D 98, 045015 (2018).
  29. Chiang-Mei Chen, Sang Pyo Kim, I-Chieh Lin, Jia-Rui Sun, and Ming-Fan Wu, Spontaneous pair production in Reissner-Nordstrom black holes, Phys. Rev. D 85, 124041 (2012).
  30. Markus B. Fröb, Jaume Garriga, Sugumi Kanno, Misao Sasaki, Jiro Soda, Takahiro Tanaka, and Alexander Vilenkin, Schwinger effect in de Sitter space, J. Cosmol. Astropart. Phys. 04 (2014) 009.
  31. Víctor M. Villalba, Creation of spin-1/2 particles by an electric field in de Sitter space, Phys. Rev. D 52, 3742 (1995).
  32. J. Garriga, Pair production by an electric field in (1+1)-dimensional de Sitter space, Phys. Rev. D 49, 6343 (1994).
  33. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982).
  34. Leonard Parker and David J. Toms, Quantum Field Theory in Curved Spacetime: Quantized Fields and Gravity (Cambridge University Press, Cambridge, England, 2009).
  35. Leonard Parker, Particle creation in expanding universes, Phys. Rev. Lett. 21, 562 (1968).
  36. L. H. Ford, Quantum field theory in curved spacetime, Rep. Prog. Phys. 84, 116901 (2021).
  37. K. Fredenhagen and R. Haag, On the derivation of Hawking radiation associated with the formation of a black hole, Commun. Math. Phys. 127, 273 (1990).
  38. L. H. Ford, Cosmological particle production: A review, Rep. Prog. Phys. 84, 116901 (2021).
  39. L. H. Ford and L. Parker, Creation of particles by singularities in asymptotically flat spacetimes, Phys. Rev. D 17, 1485 (1978).
  40. L. Parker and S. A. Fulling, Adiabatic regularization of the energy-momentum tensor of a quantized field in homogeneous spaces, Phys. Rev. D 9, 341 (1974).
  41. Philip Semrén and Greger Torgrimsson, Worldline instantons for nonperturbative particle production by space and time dependent gravitational fields, Phys. Rev. D 113, 056005 (2026).
  42. Anton Ilderton and Karthik Rajeev, Tunnelling amplitudes and Hawking radiation from worldline QFT, J. High Energy Phys. 10 (2025) 220.
  43. E. T. Akhmedov, D. V. Diakonov, and C. Schubert, Complex effective actions and gravitational pair creation, Phys. Rev. D 110, 105011 (2024).
  44. James P Edwards and Christian Schubert, Quantum mechanical path integrals in the first quantised approach to quantum field theory, arXiv:1912.10004.
  45. Christian Schubert, Perturbative quantum field theory in the string inspired formalism, Phys. Rep. 355, 73 (2001).
  46. John Joseph M. Carrasco, Yaxi Chen, Nicolas H. Pavao, and Aslan Seifi, Nonperturbative double copy: Worldline instantons, color thermality, and backreaction, arXiv:2601.17884.
  47. Anton Ilderton, William Lindved, and Karthik Rajeev, Hawking radiation from the double copy, Phys. Rev. Lett. 136, 081603 (2026).
  48. John Joseph M. Carrasco and Yaxi Chen, Double copy root of Hawking thermality, Phys. Rev. Lett. 136, 081604 (2026).
  49. Rafael Aoude, Donal O’Connell, Matteo Sergola, and Chris D. White, Hawking radiation meets the double copy, arXiv:2510.25866.
  50. François Fillion-Gourdeau, Emmanuel Lorin, and Steve MacLean, Numerical quasiconformal transformations for electron dynamics on strained graphene surfaces, Phys. Rev. E 103, 013312 (2021).
  51. X. Antoine, F. Fillion-Gourdeau, E. Lorin, and S. MacLean, Pseudospectral computational methods for the time-dependent Dirac equation in static curved space-times, J. Comput. Phys. 407, 109280 (2020).
  52. F. Fillion-Gourdeau, E. Lorin, and A. D. Bandrauk, Numerical solution of the time-dependent Dirac equation in coordinate space without fermion-doubling, J. Comput. Phys. 231, 582 (2012).
  53. Anton Ilderton, Physics of adiabatic particle number in the Schwinger effect, Phys. Rev. D 105, 016021 (2022).
  54. Gautam Mandal, Anirvan M. Sengupta, and Spentra R. Wadia, Classical solutions of 2-dimensional string theory, Mod. Phys. Lett. A 06, 1685 (1991).
  55. D. Grumiller and R. McNees, Thermodynamics of black holes in two (and higher) dimensions, J. High Energy Phys. 04 (2007) 074.
  56. V. Frolov and A. Zelnikov, Nonminimally coupled massive scalar field in a 2D black hole: Exactly solvable model, Phys. Rev. D 63, 125026 (2001).
  57. A. V. Frolov, K. R. Kristjansson, and L. Thorlacius, Global geometry of two-dimensional charged black holes, Phys. Rev. D 73, 124036 (2006).
  58. Mohammed Alkhateeb and Alex Matzkin, Microcausality and tunneling times in relativistic quantum field theory, Phys. Rev. D 112, 076005 (2025).
  59. R. E. Wagner, M. R. Ware, Q. Su, and Rainer Grobe, Bosonic analog of the Klein paradox, Phys. Rev. A 81, 024101 (2010).
  60. M. Alkhateeb, X. Gutierrez de la Cal, M. Pons, D. Sokolovski, and A. Matzkin, Relativistic quantum field theory approach to electron wave-packet tunneling: A fully causal process, Phys. Rev. A 111, 012222 (2025).
  61. F. Hebenstreit, A. Ilderton, and M. Marklund, Pair production: The view from the lightfront, Phys. Rev. D 84, 125022 (2011).
  62. R. M. Wald, Dynamics in nonglobally hyperbolic, static space-times, J. Math. Phys. (N.Y.) 21, 2802 (1980).
  63. Holger Gies and Greger Torgrimsson, Critical Schwinger pair production, Phys. Rev. Lett. 116, 090406 (2016).
  64. Holger Gies and Greger Torgrimsson, Critical Schwinger pair production. II. Universality in the deeply critical regime, Phys. Rev. D 95, 016001 (2017).
  65. J. W. Braun, Q. Su, and R. Grobe, Numerical approach to solve the time-dependent Dirac equation, Phys. Rev. A 59, 604 (1999).
  66. M. Alkhateeb, Data for fermion pair creation in two-dimensional curved spacetime (2026), https://github.com/mohammedalkhateeb-cergy/Data-for-fermion-pair-creation-in-two-dimensional-curved-spacetimes.

Outline

Information

Phys. Rev. D 113, 125002– Published 2 June, 2026
  • Received 16 February 2026
  • Accepted 27 April 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation