Skip to main content

Finding quantum effects in strong classical potentials

  • B. Manuel Hegelich (a1), Lance Labun (a1) and Ou Z. Labun (a1) (a2)

The long-standing challenge to describing charged particle dynamics in strong classical electromagnetic fields is how to incorporate classical radiation, classical radiation reaction and quantized photon emission into a consistent unified framework. The current, semiclassical methods to describe the dynamics of quantum particles in strong classical fields also provide the theoretical framework for fundamental questions in gravity and hadron–hadron collisions, including Hawking radiation, cosmological particle production and thermalization of particles created in heavy-ion collisions. However, as we show, these methods break down for highly relativistic particles propagating in strong fields. They must therefore be improved and adapted for the description of laser–plasma experiments that typically involve the acceleration of electrons. Theory developed from quantum electrodynamics, together with dedicated experimental efforts, offer the best controllable context to establish a robust, experimentally validated foundation for the fundamental theory of quantum effects in strong classical potentials.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Finding quantum effects in strong classical potentials
      Available formats
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Finding quantum effects in strong classical potentials
      Available formats
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Finding quantum effects in strong classical potentials
      Available formats
Corresponding author
Email address for correspondence:
Hide All
Akkermans, E. & Dunne, G. V. 2012 Ramsey fringes and time-domain multiple-slit interference from vacuum. Phys. Rev. Lett. 108, 030401.
Anderson, P. R. & Mottola, E. 2014a Instability of global de Sitter space to particle creation. Phys. Rev. D 89, 104038.
Anderson, P. R. & Mottola, E. 2014b Quantum vacuum instability of eternal de Sitter space. Phys. Rev. D 89, 104039.
Andersson, B., Gustafson, G., Ingelman, G. & Sjostrand, T. 1983 Parton fragmentation and string dynamics. Phys. Rep. 97, 31145.
Arefiev, A. V., Cochran, G. E., Schumacher, D. W., Robinson, A. P. L. & Chen, G. 2016 Criterion for correctly simulating relativistic electron motion in a high-intensity laser field. AIP Conf. Proc. 1777, 050001.
Bamber, C., Boege, S. J., Koffas, T., Kotseroglou, T., Melissinos, A. C., Meyerhofer, D. D., Reis, D. A., Ragg, W., Bula, C., McDonald, K. T. et al. 1999 Studies of nonlinear QED in collisions of 46.6 GeV electrons with intense laser pulses. Phys. Rev. D 60, 092004.
Brout, R., Massar, S., Parentani, R. & Spindel, P. 1995 A Primer for black hole quantum physics. Phys. Rep. 260, 329454.
Brown, L. S. & Kibble, T. W. B. 1964 Interaction of intense laser beams with electrons. Phys. Rev. 133, A705A719.
Bula, C. et al. 1996 Observation of nonlinear effects in Compton scattering. Phys. Rev. Lett. 76, 31163119.
Bulanov, S. S., Esirkepov, T. Z., Thomas, A. G. R., Koga, J. K. & Bulanov, S. V. 2010 On the Schwinger limit attainability with extreme power lasers. Phys. Rev. Lett. 105, 220407.
Cohen, T. D. & McGady, D. A. 2008 The Schwinger mechanism revisited. Phys. Rev. D 78, 036008.
Cooper, F. & Mottola, E. 1989 Quantum back reaction in scalar QED as an initial value problem. Phys. Rev. D 40, 456464.
Di Piazza, A. 2014 Ultrarelativistic electron states in a general background electromagnetic field. Phys. Rev. Lett. 113, 040402.
Di Piazza, A., Hatsagortsyan, K. Z. & Keitel, C. H. 2010 Quantum radiation reaction effects in multiphoton Compton scattering. Phys. Rev. Lett. 105, 220403.
Di Piazza, A., Muller, C., Hatsagortsyan, K. Z. & Keitel, C. H. 2012 Extremely high-intensity laser interactions with fundamental quantum systems. Rev. Mod. Phys. 84, 11771228, arXiv:1111.3886.
Dinu, V., Heinzl, T. & Ilderton, A. 2012 Infra-red divergences in plane wave backgrounds. Phys. Rev. D 86, 085037.
Dirac, P. A. M. 1938 Classical theory of radiating electrons. Proc. R. Soc. Lond. A 167, 148169.
Dunne, G. V. 2009 New strong-field QED effects at ELI: nonperturbative vacuum pair production. Eur. Phys. J. D 55, 327340.
Dunne, G. V. & Hall, T. M. 1999 Borel summation of the derivative expansion and effective actions. Phys. Rev. D 60, 065002.
Elkina, N. V., Fedotov, A. M., Kostyukov, I. Y., Legkov, M. V., Narozhny, N. B., Nerush, E. N. & Ruhl, H. 2011 QED cascades induced by circularly polarized laser fields. Phys. Rev. ST Accel. Beams 14, 054401.
Euler, H. & Kockel, B. 1935 Ueber die Streuung von Licht an Licht nach der Diracschen Theorie. Naturwissenschaft 23, 246247.
Fedotov, A. M., Narozhny, N. B., Mourou, G. & Korn, G. 2010 Limitations on the attainable intensity of high power lasers. Phys. Rev. Lett. 105, 080402.
Feynman, R. P. 1966 The development of the space-time view of quantum electrodynamics. Science 153 (3737), 699708 (World Sci. Ser. 20th Cent. Phys. 27, 9 (2000)).
Fliegner, D., Reuter, M., Schmidt, M. G. & Schubert, C. 1997 The two loop Euler–Heisenberg Lagrangian in dimensional renormalization. Theor. Math. Phys. 113, 14421451 (Teor. Mat. Fiz. 113, 289 (1997)), arXiv:hep-th/9704194.
Gelis, F. 2014 The initial stages of heavy ion collisions. Acta Phys. Polon. B 45 (12), 22572306.
Gelis, F. & Tanji, N. 2016 Schwinger mechanism revisited. Prog. Part. Nucl. Phys. 87, 149.
Gies, H. & Shaisultanov, R. 2000 On the axial current in an electromagnetic field and low-energy neutrino – photon interactions. Phys. Rev. D 62, 073003.
Gonoskov, A., Bastrakov, S., Efimenko, E., Ilderton, A., Marklund, M., Meyerov, I., Muraviev, A., Sergeev, A., Surmin, I. & Wallin, E. 2015 Extended particle-in-cell schemes for physics in ultrastrong laser fields: review and developments. Phys. Rev. E 92 (2), 023305.
Hadad, Y., Labun, L., Rafelski, J., Elkina, N., Klier, C. & Ruhl, H. 2010 Effects of radiation-reaction in relativistic laser acceleration. Phys. Rev. D 82, 096012.
Harding, A. K. & Lai, D. 2006 Physics of strongly magnetized neutron stars. Rep. Prog. Phys. 69, 26312708.
Harvey, C., Heinzl, T., Ilderton, A. & Marklund, M. 2012 Intensity-dependent electron mass shift in a laser field: existence, universality, and detection. Phys. Rev. Lett. 109, 100402.
Harvey, C. N., Ilderton, A. & King, B. 2015 Testing numerical implementations of strong field electrodynamics. Phys. Rev. A 91 (1), 013822.
Hebenstreit, F., Berges, J. & Gelfand, D. 2013 Simulating fermion production in $1+1$ dimensional QED. Phys. Rev. D 87 (10), 105006.
Hegelich, B. M., Mourou, G. & Rafelski, J. 2014 Probing the quantum vacuum with ultra intense laser pulses. Eur. Phys. J. ST 223 (6), 10931104.
Heinzl, T., Ilderton, A. & Marklund, M. 2010a Finite size effects in stimulated laser pair production. Phys. Lett. B 692, 250256.
Heinzl, T., Seipt, D. & Kampfer, B. 2010b Beam-shape effects in nonlinear Compton and Thomson scattering. Phys. Rev. A 81, 022125.
Heisenberg, W. & Euler, H. 1936 Consequences of Dirac’s theory of positrons. Z. Phys. 98, 714732.
Ilderton, A. 2011 Trident pair production in strong laser pulses. Phys. Rev. Lett. 106, 020404.
Ilderton, A. & Torgrimsson, G. 2013 Scattering in plane-wave backgrounds: infra-red effects and pole structure. Phys. Rev. D 87, 085040.
Ilderton, A., Torgrimsson, G. & Wårdh, J. 2015 Nonperturbative pair production in interpolating fields. Phys. Rev. D 92 (6), 065001.
Jansen, M. J. A. & Mller, C. 2016 Strong-field breit-wheeler pair production in short laser pulses: identifying multiphoton interference and carrier-envelope-phase effects. Phys. Rev. D 93 (5), 053011.
Keldysh, L. V. 1965 Diagram technique for nonequilibrium processes. Sov. Phys. JETP 20, 10181030.
Kharzeev, D., Levin, E. & Tuchin, K. 2007 Multi-particle production and thermalization in high-energy QCD. Phys. Rev. C 75, 044903.
Kim, S. P. 2007 Hawking radiation as quantum tunneling in Rindler coordinate. JHEP 11, 048.
King, B. & Ruhl, H. 2013 Trident pair production in a constant crossed field. Phys. Rev. D 88 (1), 013005.
Klein, O. 1929 Die Reflexion von Elektronen an einem Potentialsprung nach der relativistischen Dynamik von Dirac. Z. Phys. 53, 157165.
Kluger, Y., Eisenberg, J. M., Svetitsky, B., Cooper, F. & Mottola, E. 1992 Fermion pair production in a strong electric field. Phys. Rev. D 45, 46594671.
Kluger, Y., Mottola, E. & Eisenberg, J. M. 1998 The quantum Vlasov equation and its Markov limit. Phys. Rev. D 58, 125015.
Labun, L. & Rafelski, J. 2009 Vacuum decay time in strong external fields. Phys. Rev. D 79, 057901.
Labun, L. & Rafelski, J. 2010 Dark energy simulacrum in nonlinear electrodynamics. Phys. Rev. D 81, 065026.
Labun, L. & Zhang, O.2017 (in preparation).
Landau, L. D. & Lifshitz, E. M. 1989 The Classical Theory of Fields, 4th edn. 481p. Pergamon.
Lavelle, M., McMullan, D. & Raddadi, M. 2013 Propagation in an intense background. Phys. Rev. D 87 (8), 085024.
Mackenroth, F. & Di Piazza, A. 2011 Nonlinear Compton scattering in ultra-short laser pulses. Phys. Rev. A 83, 032106.
Mackenroth, F. & Di Piazza, A. 2013 Nonlinear double Compton scattering in the ultrarelativistic quantum regime. Phys. Rev. Lett. 110 (7), 070402.
Meuren, S., Hatsagortsyan, K. Z., Keitel, C. H. & Di Piazza, A. 2015a High-energy recollision processes of laser-generated electron-positron pairs. Phys. Rev. Lett. 114 (14), 143201.
Meuren, S., Hatsagortsyan, K. Z., Keitel, C. H. & Di Piazza, A. 2015b Polarization operator approach to pair creation in short laser pulses. Phys. Rev. D 91 (1), 013009.
Meuren, S., Keitel, C. H. & Di Piazza, A. 2013 Polarization operator for plane-wave background fields. Phys. Rev. D 88 (1), 013007.
Meuren, S., Keitel, C. H. & Di Piazza, A. 2015c Nonlinear neutrino-photon interactions inside strong laser pulses. JHEP 06, 127, arXiv:1504.02722.
Meuren, S., Keitel, C. H. & Di Piazza, A. 2016 Semiclassical picture for electron-positron photoproduction in strong laser fields. Phys. Rev. D 93 (8), 085028.
Morozov, D. A., Narozhnyi, N. B. & Ritus, V. I. 1981 Vertex function of electron in a constant electromagnetic field. Sov. Phys. JETP 53, 11031130.
Nousch, T., Seipt, D., Kampfer, B. & Titov, A. I. 2012 Pair production in short laser pulses near threshold. Phys. Lett. B 715, 246250.
Peskin, M. E. & Schroeder, D. V. 1995 An Introduction to Quantum Field Theory. Addison-Wesley.
Reuter, M., Schmidt, M. G. & Schubert, C. 1997 Constant external fields in gauge theory and the spin 0, $1/2$ , 1 path integrals. Ann. Phys. 259, 313365.
Ritus, V. I. 1972 Radiative corrections in quantum electrodynamics with intense field and their analytical properties. Ann. Phys. 69, 555.
Ritus, V. I. 1975 The Lagrange function of an intensive electromagnetic field and quantum electrodynamics at short distances. Sov. Phys. JETP 42, 774813.
Ritus, V. I. 1985 Quantum effects of the interaction of elementary particles with an intense electromagnetic field. J. Russ. Laser Res. 6, 497.
Sauter, F. 1931 Uber das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs. Z. Phys. 69, 742764.
Schutzhold, R., Gies, H. & Dunne, G. 2008 Dynamically assisted Schwinger mechanism. Phys. Rev. Lett. 101, 130404.
Schwinger, J. S. 1951 On gauge invariance and vacuum polarization. Phys. Rev. 82, 664679.
Seipt, D. & Kampfer, B. 2011 Non-linear compton scattering of ultrashort and ultraintense laser pulses. Phys. Rev. A 83, 022101.
Seipt, D. & Kampfer, B. 2012 Two-photon Compton process in pulsed intense laser fields. Phys. Rev. D 85, 101701.
Shaisultanov, R. 1998 Photon neutrino interactions in magnetic field. Phys. Rev. Lett. 80, 15861587.
Shaisultanov, R. 2000 The neutrino neutrino gamma amplitude in an external homogeneous electromagnetic field. Phys. Rev. D 62, 113005.
Titov, A. I., Takabe, H., Kampfer, B. & Hosaka, A. 2012 Enhanced subthreshold electron-positron production in short laser pulses. Phys. Rev. Lett. 108, 240406.
Wolkow, D. M. 1935 Uber eine Klasse von Losungen der Diracschen Gleichung. Z. Phys. 94, 250260.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Plasma Physics
  • ISSN: 0022-3778
  • EISSN: 1469-7807
  • URL: /core/journals/journal-of-plasma-physics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Altmetric attention score

Full text views

Total number of HTML views: 23
Total number of PDF views: 143 *
Loading metrics...

Abstract views

Total abstract views: 408 *
Loading metrics...

* Views captured on Cambridge Core between 29th May 2017 - 19th March 2018. This data will be updated every 24 hours.