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1. Internal symmetries isospin symmetry => nuclear physics SU(3) – symmetry =>hadrons chiral summetry => pions color symmetry =>quarks electroweak.

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Presentation on theme: "1. Internal symmetries isospin symmetry => nuclear physics SU(3) – symmetry =>hadrons chiral summetry => pions color symmetry =>quarks electroweak."— Presentation transcript:

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5 Internal symmetries isospin symmetry => nuclear physics SU(3) – symmetry =>hadrons chiral summetry => pions color symmetry =>quarks electroweak symmetry => SU(2)xU(1) model >

6 Internal symmetries: broken by interaction ( electromagnetism breaks isospin ) broken by explicit symmetry breaking ( SU(3) – symmetry of hadrons ) unbroken ( color symmetry of quarks ) broken by spontaneous symmetry breaking ( chiral symmetry and electroweak symmetry)

7 Rutherford: He suggested in 1919 that there must exist a neutral partner of the proton. helium nucleus: charge: 2 x proton mass: 4 x proton

8 1932: discovery of the neutron (J. Chadwick) atomic nuclei are composed of protons and neutrons

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10 nucleons: doublet of SU(2)

11 Lawrence Berkeley Nat. Lab

12 1953 pion nucleus

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14 delta: quadruplet ( 1230 MeV )

15 pions: triplet eta: singlet

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19 U(n): group of complex unitary n x n matrices SU(n): n x n matrices with det U = 1

20 U = exp (iH) H: Hermitean n x n matrix

21 det U = exp i (trH) SU(n): det U = 1 tr H = 0

22 SU(n): (n x n - 1) generators SU(2): 3 SU(3): 8 SU(4): 15 SU(5): 24

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31  quarks triplet  fundamental representation

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33  hypercharge

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35 quark triplet

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37 irreducible representations choose state with maximal value of t(3) – proceed into the U, T and V directions to the left, until it stops

38 steps p and q External line of representation

39 each state is described by 3 numbers:

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48 * * 15* * 24* 42* 64

49 direct product of representations

50 invariant operator e.g. for angular momentum

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52 1  0 3,3*  4/3 6,6*  10/3 8  3 10,10*  6 27  8

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59 Bevatron in Berkeley

60 K-mesons: 1947 => Eta-meson: 1961

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69 breaking of SU(3): much larger than the breaking of isospin symmetry

70 MeV 1190 MeV 1318 MeV 1116 MeV

71 71 ??? 1232 MeV 1530 MeV 1385 MeV

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73 Physics given by a(t) - the various matrix elements => Clebsch-Gordan coefficients

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76  f - coupling  d - coupling Wigner-Eckart theorem -- SU(3)

77 Susumu Okubo (Rochester)

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82 MeV 1672 MeV ? 1232 MeV 1530 MeV 1385 MeV

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85 MeV 138 MeV 958 MeV548 MeV 496 MeV

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87 mixing changes the masses lower state  lower higher state  higher Experiment: mixing angle about 16 degrees

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90 Why pi mesons have a small mass? Gell-Mann, Oakes, Renner (1968) Chiral Symmetry SU(3) => SU(3,L) x SU(3,R)

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92 Chiral symmetry breaking: all eight mesons acquire masses

93 SU(3,L) x SU(3,R) SU(2,L) x SU(2,R) SU(2) K-mesons and eta meson massive pions massless pions massive

94 Why chiral symmetry?  QCD


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