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The Standard Model of Particle Physics and Beyond

-. 10 lectures. The Standard Model of Particle Physics and Beyond. H. Fritzsch. classical physics : a physical system is given by the functions of the coordinates and of the associated momenta –.

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The Standard Model of Particle Physics and Beyond

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  1. - 10 lectures The Standard Model of Particle Physics and Beyond H. Fritzsch

  2. classicalphysics:a physicalsystemisgivenbythefunctionsofthecoordinatesandoftheassociatedmomenta –

  3. quantumphysics:coordinatesandmomentaareHermiteanoperators in theHilbert spaceofstates

  4. 1927: Schrödinger equation for the wave function Erwin Schrödinger

  5. harmonicoscillator

  6. Oscillator classical

  7. Gauß curve

  8. Symmetryin Quantum Physics

  9. A. externalsymmetriesB. internalsymmetries

  10. externalsymmetries:Poincare group conservationlaws: energy momentum angular momentum

  11. externalsymmetries:exact in Minkowskispace

  12. General Relativity:noenergyconservationnomomentumconservationnoconservationof angularmomentum

  13. internalsymmetries:IsospinSU(3)Color symmetryElectroweakgaugesymmetryGrand Unification: SO(10)Supersymmetry

  14. internalsymmetriesbrokenbyinteraction: isospinbrokenbyquarkmasses: SU(3)brokenby SSB: electroweaksymmetryunbroken: colorsymmetry

  15. symmetriesaredescribedmathematicallybygroups

  16. symmetrygroups n finite or infinite

  17. examples of groups: integer numbers: 3 + 5=8, 3 + 0=3, 5 + (-5) = 0 real numbers: 3.20 x 2.70=8.64, 3.20 x 1 = 3.20 3.20 x 0.3125 = 1

  18. Niels Abel Norway 19th century

  19. A symmetryisa transformationof thedynamical variables, whichleavethe action invariant.

  20. Classicalmechanics:  translationsof spaceand time – ( energy, momentum ) rotationsofspace ( angular momentum )

  21. Special Relativity => Poincare group: translationsof 4 space - time coordinates + Lorentz transformations

  22. Henri Poincare late19th century

  23. Symmetry in quantum physics ( E. Wigner, 1930 … ) U: unitary operator

  24. Eugene Wigner Nobel prize 1964

  25. Poincare group P:- time translations -- spacetranslations -- rotationsofspace -- „rotation“ betweentime andspace -

  26. e.g. rotationsofspace: - - SO(3)< P

  27. Casimir operatorof Poincare group

  28. symmetry U The operator U commutes with the Hamiltonoperator H: If U acts on a wave function with a specific energy, the new wave function must have the same energy ( degenerate energy levels ).

  29. discretesymmetries P ~ paritysymmetry CP - symmetry CPT - symmetry

  30. P: exactsymmetry in the strong andelectromagneticinteractions

  31. P:maximal violationin theweakinteractions

  32. theoryofparityviolation:1956: T. D. Lee andC.N.Yangexperiment: Chien-Shiung Wu( Columbia university )

  33. Lee Yang Wu

  34. Experiment of Wu:betadecayofcobalt

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