Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 6 (2010), 041, 27 pages      arXiv:1003.4184      http://dx.doi.org/10.3842/SIGMA.2010.041
Contribution to the Special Issue “Noncommutative Spaces and Fields”

Strong Field, Noncommutative QED

Anton Ilderton, Joakim Lundin and Mattias Marklund
Department of Physics, Umeå University, 901-87 Umeå, Sweden

Received March 23, 2010, in final form May 17, 2010; Published online May 26, 2010

Abstract
We review the effects of strong background fields in noncommutative QED. Beginning with the noncommutative Maxwell and Dirac equations, we describe how combined noncommutative and strong field effects modify the propagation of fermions and photons. We extend these studies beyond the case of constant backgrounds by giving a new and revealing interpretation of the photon dispersion relation. Considering scattering in background fields, we then show that the noncommutative photon is primarily responsible for generating deviations from strong field QED results. Finally, we propose a new method for constructing gauge invariant variables in noncommutative QED, and use it to analyse the physics of our null background fields.

Key words: noncommutative QED; background fields.

pdf (476 kb)   ps (334 kb)   tex (193 kb)

References

  1. Heinzl T., Ilderton A., Exploring high-intensity QED at ELI, Eur. Phys. J. D 55 (2009), 359-364, arXiv:0811.1960.
  2. Marklund M., Lundin J., Quantum vacuum experiments using high intensity lasers, Eur. Phys. J. D 55 (2009), 319-326, arXiv:0812.3087.
  3. Landi G., An introduction to noncommutative spaces and their geometries, Lecture Notes in Physics. New Series m: Monographs, Vol. 51, Springer-Verlag, Berlin, 1997, hep-th/9701078.
  4. Douglas M.R., Nekrasov N.A., Noncommutative field theory, Rev. Modern Phys. 73 (2001), 977-1029, hep-th/0106048.
  5. Szabo R.J., Quantum field theory on noncommutative spaces, Phys. Rep. 378 (2003), 207-299, hep-th/0109162.
  6. Szabo R.J., Magnetic backgrounds and noncommutative field theory, Internat. J. Modern Phys. A 19 (2004), 1837-1861, physics/0401142.
  7. Carroll S.M., Harvey J.A., Kostelecký V.A., Lane C.D., Okamoto T., Noncommutative field theory and Lorentz violation, Phys. Rev. Lett. 87 (2001), 141601, 4 pages, hep-th/0105082.
  8. Szabo R.J., Quantum gravity, field theory and signatures of noncommutative spacetime, arXiv:0906.2913.
  9. Kouveliotou C. et al., An X-ray pulsar with a superstrong magnetic field in the soft γ-ray repeater SGR 1806-20, Nature 393 (1998), 235-237.
  10. Palmer D.M. et al., A giant γ-ray flare from the magnetar SGR 1806-20, Nature 434 (2005), 1107-1109, astro-ph/0503030.
  11. Baring M.G., Harding A.K., Photon splitting and pair creation in highly magnetized pulsars, Astrophys. J. 547 (2001), 929-948, astro-ph/0010400.
  12. Aharony O., Gomis J., Mehen T., On theories with light-like noncommutativity, J. High Energy Phys. 2000 (2000), no. 9, 023, 15 pages, hep-th/0006236.
  13. Gomis J., Mehen T., Space-time noncommutative field theories and unitarity, Nuclear Phys. B 591 (2000), 265-276, hep-th/0005129.
  14. Bahns D., Doplicher S., Fredenhagen K., Piacitelli G., On the unitarity problem in space/time noncommutative theories, Phys. Lett. B 533 (2002), 178-181, hep-th/0201222.
  15. Heinzl T., Ilderton A., Marklund M., Noncommutativity and the lightfront, Nuclear Phys. Proc. Suppl. 199 (2010), 153-159, arXiv:0908.2917.
  16. Furry W.H., On bound states and scattering in positron theory, Phys. Rev. 81 (1951), 115-124.
  17. Moortgat-Pick G., The Furry picure, J. Phys. Conf. Ser. 198 (2009), 012002, 7 pages.
  18. Heinzl T., Ilderton A., A Lorentz and gauge invariant measure of laser intensity, Opt. Comm. 282 (2009), 1879-1883, arXiv:0807.1841.
  19. McDonald K.T., Proposal for experimental studies of nonlinear quantum electrodynamics, available at http://www.hep.princeton.edu/~mcdonald/e144/prop.pdf.
  20. Nikishov A.I., Ritus V.I., Quantum processes in the field of a plane electromagnetic wave and in a constant field. I, Zh. Eksper. Teoret. Fiz. 46 (1963), 776-796 (English transl.: Sov. Phys. JETP 19 (1964), 529-541).
  21. Nikishov A.I., Ritus V.I., Quantum processes in the field of a plane electromagnetic wave and in a constant field. II, Zh. Eksper. Teoret. Fiz. 46 (1964), 1768-1781 (English transl.: Sov. Phys. JETP 19 (1964), 1191-1199).
  22. Narozhnyi N.B., Nikishov A.I., Ritus V.I., Quantum processes in the field of a circularly polarized electromagnetic wave, Zh. Eksper. Teoret. Fiz. 47 (1964), 930-940 (English transl.: Sov. Phys. JETP 20 (1965), 622-629).
  23. Harvey C., Heinzl T., Ilderton A., Signatures of high-intensity Compton scattering, Phys. Rev. A 79 (2009), 063407, 17 pages, arXiv:0903.4151.
  24. Heinzl T., Ilderton A., Marklund M., Finite size effects in stimulated laser pair production, arXiv:1002.4018.
  25. Toll J., The dispersion relation for light and its application to problems involving electron pairs, PhD Thesis, Princeton, 1952.
  26. Heinzl T., Liesfeld B., Amthor K.U., Schwoerer H., Sauerbrey R., Wipf A., On the observation of vacuum birefringence, Opt. Comm. 267 (2006), 318-321, hep-ph/0601076.
  27. Abel S.A., Jaeckel J., Khoze V.V., Ringwald A., Vacuum birefringence as a probe of Planck scale noncommutativity, J. High Energy Phys. 2006 (2006), no. 9, 074, 18 pages, hep-ph/0607188.
  28. Seiberg N., Witten E., String theory and noncommutative geometry, J. High Energy Phys. 1999 (1999), no. 9, 032, 93 pages, hep-th/9908142.
  29. Gross D.J., Hashimoto A., Itzhaki N., Observables of non-commutative gauge theories, Adv. Theor. Math. Phys. 4 (2000), 893-928, hep-th/0008075.
  30. Langmann E., Szabo R.J., Teleparallel gravity and dimensional reductions of noncommutative gauge theory, Phys. Rev. D 64 (2001), 104019, 15 pages, hep-th/0105094.
  31. Hayakawa M., Perturbative analysis on infrared aspects of noncommutative QED on R4, Phys. Lett. B 478 (2000), 394-400, hep-th/9912094.
  32. Hayakawa M., Perturbative analysis on infrared and ultraviolet aspects of noncommutative QED on R4, hep-th/9912167.
  33. Hewett J.L., Petriello F.J., Rizzo T.G., Signals for non-commutative interactions at linear colliders, Phys. Rev. D 64 (2001), 075012, 23 pages, hep-ph/0010354.
  34. Ardalan F., Sadooghi N., Anomaly and nonplanar diagrams in noncommutative gauge theories, Internat. J. Modern Phys. A 17 (2002), 123-144, hep-th/0009233.
  35. Nakajima T., Conformal anomalies in noncommutative gauge theories, Phys. Rev. D 66 (2002), 085008, 9 pages, hep-th/0108158.
  36. Minwalla S., Van Raamsdonk M., Seiberg N., Noncommutative perturbative dynamics, J. High Energy Phys. 2000 (2000), no. 2, 020, 31 pages, hep-th/9912072.
  37. Matusis A., Susskind L., Toumbas N., The IR/UV connection in the non-commutative gauge theories, J. High Energy Phys. 2000 (2000), no. 12, 002, 18 pages, hep-th/0002075.
  38. Martín C.P., Sánchez-Ruiz D., One-loop UV divergent structure of U(1) Yang-Mills theory on noncommutative R4, Phys. Rev. Lett. 83 (1999), 476-479, hep-th/9903077.
  39. Grosse H., Wulkenhaar R., Renormalisation of φ4 theory on noncommutative R4 in the matrix base, Comm. Math. Phys. 256 (2005), 305-374, hep-th/0401128.
  40. de Goursac A., On the origin of the harmonic term in noncommutative quantum field theory, arXiv:1003.5788.
  41. de Goursac A., Wallet J.-C., Wulkenhaar R., Noncommutative induced gauge theory, Eur. Phys. J. C 51 (2007), 977-987, hep-th/0703075.
  42. Grosse H., Wohlgenannt M., Induced gauge theory on a noncommutative space, Eur. Phys. J. C 52 (2007), 435-450, hep-th/0703169.
  43. de Goursac A.M., Noncommutative geometry, gauge theory and renormalization, PhD Thesis, arXiv:0910.5158.
  44. Grosse H., Wohlgenannt M., Noncommutative QFT and renormalization, J. Phys. Conf. Ser. 53 (2006), 764-792, hep-th/0607208.
  45. Rivasseau V., Vignes-Tourneret F., Renormalisation of non-commutative field theories, hep-th/0702068.
  46. Blaschke D.N., Kronberger E., Rofner A., Schweda M., Sedmik R.I.P., Wohlgenannt M., On the problem of renormalizability in non-commutative gauge field models - a critical review, Fortschr. Phys. 58 (2010), 364-372, arXiv:0908.0467.
  47. Fischer A., Szabo R.J., UV/IR duality in noncommutative quantum field theory, arXiv:1001.3776.
  48. Langmann E., Szabo R.J., Duality in scalar field theory on noncommutative phase spaces, Phys. Lett. B 533 (2002), 168-177, hep-th/0202039.
  49. Blaschke D.N., Gieres F., Kronberger E., Schweda M., Wohlgenannt M., Translation-invariant models for non-commutative gauge fields, J. Phys. A: Math. Theor. 41 (2008), 252002, 7 pages, arXiv:0804.1914.
  50. Schupp P., You J., UV/IR mixing in noncommutative QED defined by Seiberg-Witten map, J. High Energy Phys. 2008 (2008), no. 8, 107, 10 pages, arXiv:0807.4886.
  51. Raasakka M., Tureanu A., On UV/IR mixing via Seiberg-Witten map for noncommutative QED, arXiv:1002.4531.
  52. Alvarez-Gaumé L., Barbón J.L.F., Non-linear vacuum phenomena in non-commutative QED, Internat. J. Modern Phys. A 16 (2001), 1123-1146, hep-th/0006209.
  53. Wolkow D., Über eine Klasse von Lösungen der Diracschen Gleichung, Z. Phys. 94 (1935), 250-260.
  54. Barbón J.L.F., Introduction to noncommutative field theory, in Proceedings of ICTP Summer School in Particle Physics (Trieste, Italy, June 18 - July 6, 2001), Editors A. Masiero, G. Senjanovic, A.Yu. Smirnov, G. Thompson, ICTP Lecture Note Series, Vol. 10, Trieste, 2002, 185-219.
  55. Gerhold A., Grimstrup J., Grosse H., Popp L., Schweda M., Wulkenhaar R., The energy-momentum tensor on noncommutative spaces: some pedagogical comments, hep-th/0012112.
  56. Das A.K., Frenkel J., Energy-momentum tensor in non-commutative gauge theories, Phys. Rev. D 67 (2003), 067701, 3 pages, hep-th/0212122.
  57. Brown L.S., Kibble T.W.B., Interaction of intense laser beams with electrons, Phys. Rev. 133 (1964), A705-A719.
  58. Reiss H.R., Eberly J.H., Green's function in intense-field electrodynamics, Phys. Rev. 151 (1966), 1058-1066.
  59. Dymarsky A.Y., Noncommutative field theory in formalism of first quantization, Phys. Lett. B 527 (2002), 125-130, hep-th/0104250.
  60. Coleman S., Non-Abelian plane waves, Phys. Lett. B 70 (1977), 59-60.
  61. Mariz T., Nascimento J.R., Rivelles V.O., Dispersion relations in noncommutative theories, Phys. Rev. D 75 (2007), 025020, 7 pages, hep-th/0609132.
  62. Guralnik Z., Jackiw R., Pi S.Y., Polychronakos A.P., Testing non-commutative QED, constructing non-commutative MHD, Phys. Lett. B 517 (2001), 450-456, hep-th/0106044.
  63. Chatillon N., Pinzul A., Light propagation in a background field for time-space non-commutativity and axionic non-commutative QED, Nuclear Phys. B 764 (2007), 95-108, hep-ph/0607243.
  64. Abbott L.F., Introduction to the background field method, Acta Phys. Polon. B 13 (1982), 33-50.
  65. Fatollahi A.H., Jafari A., On the bound states of photons in noncommutative U(1) gauge theory, Eur. Phys. J. C 46 (2006), 235-245, hep-th/0503078.
  66. Volkholz J., Bietenholz W., Nishimura J., Susaki Y., The scaling of QED in a non-commutative space-time, PoS LAT2005 (2005), 264, 6 pages, hep-lat/0509146.
  67. Gomis J., Landsteiner K., Lopez E., Non-relativistic non-commutative field theory and UV/IR mixing, Phys. Rev. D 62 (2000), 105006, 6 pages, hep-th/0004115.
  68. Baek S., Ghosh D.K., He X.G., Hwang W.Y.P., Signatures of non-commutative QED at photon colliders, Phys. Rev. D 64 (2001), 056001, 7 pages, hep-ph/0103068.
  69. Godfrey S., Doncheski M.A., Signals for non-commutative QED in eγ and γγ collisions, Phys. Rev. D 65 (2002), 015005, 9 pages, hep-ph/0108268.
  70. Godfrey S., Doncheski M.A., Signals for non-commutative QED in eγ and γγ collisions, in Proceedings of the APS/DPF/DPB Summer Study on the Future of Particle Physics (Snowmass, 2001), Editor N. Graf, 2001, P313, 4 pages, hep-ph/0111147.
  71. Ohl T., Reuter J., Testing the noncommutative standard model at a future photon collider, Phys. Rev. D 70 (2004), 076007, 10 pages, hep-ph/0406098.
  72. Sauter F., Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs, Z. Phys. 69 (1931), 742-764.
  73. Schwinger J.S., On gauge invariance and vacuum polarization, Phys. Rev. 82 (1951), 664-679.
  74. Chair N., Sheikh-Jabbari M.M., Pair production by a constant external field in noncommutative QED, Phys. Lett. B 504 (2001), 141-146, hep-th/0009037.
  75. Riad I.F., Sheikh-Jabbari M.M., Noncommutative QED and anomalous dipole moments, J. High Energy Phys. 2000 (2000), no. 8, 045, 22 pages, hep-th/0008132.
  76. Heinzl T., Ilderton A., Marklund M., Laser intensity effects in noncommutative QED, Phys. Rev. D 81 (2010), 051902, 5 pages, arXiv:0909.0656.
  77. Hebenstreit F., Alkofer R., Dunne G.V., Gies H., Momentum signatures for Schwinger pair production in short laser pulses with sub-cycle structure, Phys. Rev. Lett. 102 (2009), 150404, 4 pages, arXiv:0901.2631.
  78. Heinzl T., Seipt D., Kampfer B., Beam-shape effects in nonlinear Compton and Thomson scattering, Phys. Rev. A 81 (2010), 022125, 17 pages, arXiv:0911.1622.
  79. Mackenroth F., Di Piazza A., Keitel C.H., Determining the carrier-envelope phase of short intense laser pulses, arXiv:1001.3614.
  80. Das S.R., Rey S.J., Open Wilson lines in noncommutative gauge theory and tomography of holographic dual supergravity, Nuclear Phys. B 590 (2000), 453-470, hep-th/0008042.
  81. Lavelle M., McMullan D., Constituent quarks from QCD, Phys. Rep. 279 (1997), 1-65, hep-ph/9509344.
  82. Dirac P.A.M., Gauge-invariant formulation of quantum electrodynamics, Canad. J. Phys. 33 (1955), 650-660.
  83. Bagan E., Lavelle M., McMullan D., Charges from dressed matter: construction, Ann. Physics 282 (2000), 471-502, hep-ph/9909257.
  84. Bagan E., Lavelle M., McMullan D., Charges from dressed matter: physics and renormalisation, Ann. Physics 282 (2000), 503-540, hep-ph/9909262.
  85. Ilderton A., Lavelle M., McMullan D., Colour, copies and confinement, J. High Energy Phys. 2007 (2007), no. 3, 044, 27 pages, hep-th/0701168.
  86. Ilderton A., Lavelle M., McMullan D., Symmetry breaking, conformal geometry and gauge invariance, arXiv:1002.1170.
  87. Langfeld K., Heinzl T., Ilderton A., Lavelle M., McMullan D., Solution of the Gribov problem from gauge invariance, PoS(CONFINEMENT8) (2008), 047, 5 pages, arXiv:0812.2418.
  88. Binosi D., Theussl L., JaxoDraw: a graphical user interface for drawing Feynman diagrams, Comput. Phys. Comm. 161 (2004), 76-86, hep-ph/0309015.
  89. Binosi D., Collins J., Kaufhold C., Theussl L., JaxoDraw: a graphical user interface for drawing Feynman diagrams. Version 2.0 release notes, Comput. Phys. Comm. 180 (2009), 1709-1715, arXiv:0811.4113.

Previous article   Next article   Contents of Volume 6 (2010)