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Gauge Theories

-. Gauge Theories. quantum electrodynamics. QED. -. Lagrangian of a free Dirac field. -. -. field strength. -. Lagrangian of QED:. interaction. gauge theory. e. -. fine-structure constant. =0.00729735253. ~1 / 137. Feynman diagram. Quantum Field Theory:

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Gauge Theories

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  1. - Gauge Theories

  2. quantum electrodynamics QED

  3. - Lagrangianof a free Dirac field

  4. -

  5. - fieldstrength

  6. - Lagrangian of QED:

  7. interaction gauge theory

  8. e

  9. - fine-structure constant =0.00729735253 ~1 / 137

  10. Feynman diagram

  11. Quantum Field Theory: Finestructure constant  function of energy or scale due to quantum fluctuations of electron-positron pairs => partial screening of bare charge of the electron at distances less than the compton wavelength of the electron M. Gell-Mann / F. Low ( 1954 )

  12. partial screening + - + + - - - -

  13. -

  14. => alpha increases with energy +

  15. renormalization group LEP

  16. Abelean gauge theory: gauge bosons interact only with the fermions

  17. Non-Abeleangaugetheories

  18. non-Abelean gauge theory gauge bosons interact with the fermions and with the gauge bosons

  19. strong interactions QCD quantum chromodynamics

  20. M. Gell-Mann, H. Fritzsch 1971: color index for the quarks (uuu) u ==> exact symmetry c SU(3)

  21. forces between quarks: 1972: F., Gell-Mann 1973: F., Gell-Mann, Leutwyler  gauge theory in color space QCD

  22. QCD 8 gluons

  23. QCD • gluon quark

  24. LEP experiments: at 91 GeV

  25. gluon field strength self-interaction

  26. gluon quark new

  27. QCD: asymptotically free coupling at high energies ==> 0 Khriplovich (1968) t´ Hooft (1971) Gross, Wilczek (1973) Politzer (1973)

  28. QED - QCD sign !!!

  29. as in QED const. = +5 const. = -16

  30. experiment => as

  31. 3 Quarks: u,d,s coupling ==>0

  32. asymptotic freedom

  33. violation of „scaling“

  34. p: proton momentum x p: quark momentum 0 < x < 1

  35. 2 2 + + … + + … +

  36. scaling violations in QCD Q2 > Q1 Q1 The structure function data exhibit systematic violations of Bjorken scaling quarks emit gluons!

  37. violation of scaling

  38. QCD

  39. scaling violations  QCD scale

  40. infrared slavery

  41. infrared slavery Confinement

  42. quark – antiquark potential * * small distances: Coulomb potential

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