, Volume 51, Issue 3–4, pp 317–355 | Cite as

Charges in gauge theories



In this article we investigate charged particles in gauge theories. After reviewing the physical and theoretical problems, a method to construct charged particles is presented. Explicit solutions are found in the abelian theory and a physical interpretation is given. These solutions and our interpretation of these variables as the true degrees of freedom for charged particles, are then tested in the perturbative domain and are demonstrated to yield infra-red finite, on-shell Green’s functions at all orders of perturbation theory. The extension to collinear divergences is studied and it is shown that this method applies to the case of massless charged particles. The application of these constructions to the charged sectors of the standard model is reviewed and we conclude with a discussion of the successes achieved so far in this programme and a list of open questions.


Gauge theories infra-red charged particles confinement 


11.15 12.20 12.38 12.39 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    E P Wigner,Ann. Math. 40, 149 (1939)CrossRefMathSciNetGoogle Scholar
  2. [2]
    S Weinberg,The quantum theory of fields (Cambridge University Press, Cambridge, 1995)Google Scholar
  3. [3]
    D BuchholzPhys. Lett. B174, 331 (1986)ADSMathSciNetGoogle Scholar
  4. [4]
    P Kulish and L Faddeev,Theor. Math. Phys. 4, 745 (1970)CrossRefGoogle Scholar
  5. [5]
    M Lavelle and D McMullan,Phys. Rep. 279, 1 (1997), hep-ph/9509344CrossRefADSGoogle Scholar
  6. [6]
    M Ciafaloni, inQuantum chromodynamics, Edited by A H Mueller (World Scientific, Singapore, 1989)Google Scholar
  7. [7]
    V D Duca, L Magnea, and G Sterman,Nucl. Phys. B324, 391 (1989)CrossRefADSGoogle Scholar
  8. [7a]
    For this reason one sometimes speaks of mass singularitiesGoogle Scholar
  9. [8]
    UKQCD, D S Henty, O Oliveira, C Parrinello and S Ryan,Phys. Rev. D54, 6923 (1996), hep-lat/9607014ADSGoogle Scholar
  10. [9]
    S A Gogilidze, A M Khvedelidze, D M Mladenov and H P Pavel,Hamiltonian reduction of SU(2) Dirac Yang-Mills mechanics, (1997), hep-th/9707136Google Scholar
  11. [10]
    D Maison and D Zwanziger,Nucl. Phys. B91, 425 (1975)CrossRefADSMathSciNetGoogle Scholar
  12. [11]
    H Fröhlich, G Morchio and F Strocchi,Phys. Lett. B89, 61 (1979)ADSGoogle Scholar
  13. [12]
    D Zwanziger,Phys. Rev. D11, 3504 (1975)ADSGoogle Scholar
  14. [13]
    D Zwanziger,Phys. Rev. D11, 3481 (1975)ADSGoogle Scholar
  15. [14]
    G Morchio and F Strocchi,Nucl. Phys. B211, 471 (1983)CrossRefADSMathSciNetGoogle Scholar
  16. [15]
    D Buchholz,Nucl. Phys. B469, 333 (1996), hep-th/9511002CrossRefADSMathSciNetGoogle Scholar
  17. [15a]
    But not globally gauge invariant.Google Scholar
  18. [16]
    P A M Dirac,Can. J. Phys. 33, 650 (1955)MATHMathSciNetGoogle Scholar
  19. [17]
    E d’Emilio and M Mintchev,Fortschr. Phys. 32, 473 (1984)MathSciNetGoogle Scholar
  20. [18]
    E d’Emilio and M Mintchev,Fortschr. Phys. 32 503 (1984)MathSciNetGoogle Scholar
  21. [19]
    O Steinmann,Ann. Phys. 157, 232 (1984)CrossRefADSMathSciNetGoogle Scholar
  22. [20]
    L V Prokhorov and S V Shabanov,Int. J. Mod. Phys. A7, 7815 (1992)ADSGoogle Scholar
  23. [21]
    L V Prokhorov, D V Fursaev and S V Shabanov,Theor. Math. Phys. 97, 1355 (1993)CrossRefMathSciNetGoogle Scholar
  24. [22]
    T Kawai and H P Stapp,Phys. Rev. D52, 2517 (1995), quant-ph/9502007ADSGoogle Scholar
  25. [23]
    T Kawai and H P Stapp,Phys. Rev. D52, 2505 (1995).ADSGoogle Scholar
  26. [24]
    T Kawai and H P Stapp,Phys. Rev. D52, 2484 (1995), quant-ph/9503002ADSGoogle Scholar
  27. [25]
    L Lusanna and P Valtancoli,Int. J. Mod. Phys. A12, 4769 (1997), hep-th/9606078ADSMathSciNetGoogle Scholar
  28. [26]
    L Lusanna and P Valtancoli,Int. J. Mod. Phys. A12, 4797 (1997), hep-th/9606079ADSMathSciNetGoogle Scholar
  29. [27]
    T Kashiwa and N Tanimura,Phys. Rev. D56, 2281 (1997), hep-th/9612250ADSGoogle Scholar
  30. [28]
    T Kashiwa and N Tanimura,Physical states and gauge independence of the energy momentum tensor in quantum electrodynamics, (1996), hep-th/9605207.Google Scholar
  31. [29]
    G Chechelashvili, G Jorjadze, and N Kiknadze,Theor. Math. Phys. 109, 1316 (1997), hep-th/9510050CrossRefMathSciNetGoogle Scholar
  32. [30]
    P Haagensen and K Johnson,On the wave functional for two heavy color sources in Yang-Mills theory, (1997), hep-th/9702204Google Scholar
  33. [30a]
    For details, see Sect. 7 of [5] and [30]Google Scholar
  34. [31]
    K Cahill and D R Stump,Phys. Rev. D20, 540 (1979)ADSGoogle Scholar
  35. [32]
    J Dollard,J. Math. Phys. 5, 729 (1964)CrossRefADSMathSciNetGoogle Scholar
  36. [32a]
    A fuller account of this derivation of the asymptotic interaction will be presented in § 5 as part of a more general analysis that includes the case of massless matterGoogle Scholar
  37. [33]
    N N Bogolyubov and D V ShirkovGoogle Scholar
  38. [33a]
    In non-abelian gauge theories the gauge field also needs to be dressed in order for it to carryGoogle Scholar
  39. [34]
    M Lavelle and D McMullan,Phys. Lett. B371, 83 (1996), hep-ph/9509343ADSGoogle Scholar
  40. [35]
    M Lavelle and D McMullan,Phys. Lett. B329, 68 (1994), hep-th/9403147ADSGoogle Scholar
  41. [35a]
    The non-abelian appearance of this gauge transformation in QED arises from the fact that the dressing is field dependent and thus might not commute with the potentialGoogle Scholar
  42. [36]
    E Bagan, M Lavelle, and D McMullan hep-th/9712080, to appear inPhys. Rev. D [RC] (1997)Google Scholar
  43. [37]
    R Haag,Local quantum physics: fields, particles, algebras (Springer, Berlin, 1992)MATHGoogle Scholar
  44. [38]
    H Georgi,Phys. Lett. B240, 447 (1990)ADSGoogle Scholar
  45. [39]
    G Sterman,An introduction to quantum field theory (Cambridge University Press, Cambridge, 1993).Google Scholar
  46. [40]
    E Bagan, M Lavelle, and D McMullan,Phys. Rev. D56, 3732 (1997), hep-th/9602083ADSGoogle Scholar
  47. [41]
    E Bagan, B Fiol, M Lavelle, and D McMullan,Mod. Phys. Lett. A12, 1815 (1997), hep-ph/9706515, Erratum-ibid, A12 (1997) 2317ADSGoogle Scholar
  48. [42]
    T Muta,Foundations of quantum chromodynamics (World Scientific, Singapore, 1987)Google Scholar
  49. [42a]
    The Feynman rule for the vertex with the source is here taken to be unity for simplicity, it could also be given the renormalisation group invariant form, m2ϕ*ϕGoogle Scholar
  50. [42b]
    It is easy to check that the phase part of the dressing does not bring in any soft divergencesGoogle Scholar
  51. [42c]
    Note that the massless tadpole diagrams of figure 5(b) do not cancel, but they, of course, do not alter the on-shell dependence of the IR-structureGoogle Scholar
  52. [43]
    R Jackiw and L Soloviev,Phys. Rev. 27, 1485 (1968)CrossRefADSGoogle Scholar
  53. [44]
    Y L Dokshitser, V A Khoze, A H Mueller, and S I Troian,Basics of perturbative QCD (Ed. Frontieres, Gif-sur-Yvette, France, 1991)Google Scholar
  54. [45]
    R Doria, J Frenkel, and J C Taylor,Nucl. Phys. B168, 93 (1980)CrossRefADSMathSciNetGoogle Scholar
  55. [46]
    C Di’Lieto, S Gendron, I G Halliday and C T Sachrajda,Nucl. Phys. B183, 223 (1981)CrossRefADSGoogle Scholar
  56. [47]
    D Espriu and R Tarrach,Phys. Lett. B383, 482 (1996), hep-ph/9604431ADSGoogle Scholar
  57. [48]
    F Havemann,Collinear divergences and asymptotic states, Zeuthen Report No. PHE-85-14, 1985 (unpublished), scanned at KEKGoogle Scholar
  58. [49]
    M Nowakowski and A Pilaftsis,Z. Phys. C60, 121 (1993), hep-ph/9305321ADSGoogle Scholar
  59. [50]
    G S Jones,Generalised functions, First ed. (McGraw-Hill, Berkshire, 1966)MATHGoogle Scholar
  60. [51]
    R Jackiw, D Kabat and M Ortiz,Phys. Lett. B277, 148 (1992)ADSMathSciNetGoogle Scholar
  61. [52]
    I Robinson and D Rozga,J. Math. Phys. 25, 499 (1984)CrossRefADSMathSciNetGoogle Scholar
  62. [53]
    V N Gribov,Nucl. Phys. B139, 1 (1978)CrossRefADSMathSciNetGoogle Scholar
  63. [54]
    I M Singer,Commun. Math. Phys. 60, 7 (1978)MATHCrossRefADSGoogle Scholar
  64. [55]
    M Lavelle and D McMullan,Phys. Lett. B347, 89 (1995), hep-th/9412145ADSGoogle Scholar
  65. [56]
    L Chen, M Belloni, and K Haller,Phys. Rev. D55, 2347 (1997), hep-ph/9609507ADSMathSciNetGoogle Scholar
  66. [57]
    V A Khoze and W Ochs,Int. J. Mod. Phys. A12, 2949 (1997), hep-ph/9701421ADSGoogle Scholar
  67. [58]
    C Parrinello, S Petrarca, and A VladikasPhys. Lett. B268, 236 (1991)ADSGoogle Scholar
  68. [59]
    P de Forcrand and J E Hetrick,Nucl. Phys. Proc. Suppl. 42, 861 (1995), hep-lat/9412044.CrossRefADSGoogle Scholar
  69. [60]
    R G Stuart,Unstable particles, (1995), hep-ph/9504308Google Scholar
  70. [61]
    J Papavassiliou and A Pilaftsis,Phys, Rev. Lett. 75, 3060 (1995), hep-ph/9506417CrossRefADSGoogle Scholar
  71. [62]
    N Seiberg and E Witten,Nucl. Phys. B426, 19 (1994), hep-th/9407087CrossRefADSMathSciNetGoogle Scholar
  72. [63]
    M Lavelle and D McMullan,Phys. Rev. Lett. 71, 3758 (1993), hep-th/9306132CrossRefADSGoogle Scholar
  73. [64]
    I Bialynicki-Birula and Z Bialynicka-Birula,Quantum electrodynamics (Pergamon Press, Oxford, 1975)Google Scholar

Copyright information

© Indian Academy of Sciences 1998

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsThe University of PlymouthPlymouthUK

Personalised recommendations