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Weinberg Salam Model

Weinberg Salam Model. SU(2)×U(1)gauge symmetry. SU(2) gauge field. U(1) gaugefield . Higgs field. complex scalar, SU(2) doublet Y f =1. Lorentz group. quark lepton. SU(3) . U(1)hypercharge. SU(2) . quark lepton. - 1 . 1/3. 2. 3. 0. 4/3. 3. 1. - 2. - 2/3.

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Weinberg Salam Model

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  1. Weinberg Salam Model SU(2)×U(1)gauge symmetry SU(2) gaugefield U(1) gaugefield Higgsfield complex scalar,SU(2) doublet Yf=1 Lorentz group quark lepton SU(3) U(1)hypercharge SU(2) quark lepton -1 1/3 2 3 0 4/3 3 1 -2 -2/3 Lagrangian density

  2. SU(2)×U(1)gauge sym. is broken spontaneously v.e.v. redefinition gauge field mixing Weinberg angle mass of gauge fields W & Z get massive absorbing c. mass of x The electromagnetic U(1) gauge symmetry is preserved. , electromagnetic coupling constant

  3. Yukawa interaction fermion mass term

  4. diagonalization diagonal Cabibbo-Kobayashi-Maskawa matrix Maki-Nakagawa-Sakata matrix +h.c. +h.c.

  5. Path Integral Quantization cf. coordinate eigenstate fields completeness probability amplitude tn tn xn xn xn xn ti t1 ti t1 xi xi xi x1 x1 x1 xi x1

  6. Path Integral Quantization cf. coordinate H : Hamiltonian eigenstate fields completeness provability amplitude tn tn xn xn xn xn ti t1 ti t1 xi xi xi x1 x1 x1 xi x1

  7. H : Hamiltonian + O((Dti)2) H Dti Dti = fxi ・ : canonical conjugate of : canonical conjugate of eigenstate eigenstate completeness completeness

  8. H : Hamiltonian + O((Dti)2) H = pxi2/2+V = = L L : Lagrangian = S N'

  9. Path Integral Quantization cf. coordinate H : Hamiltonian eigenstate fields completeness + O((Dti)2) H provability amplitude tn tn xn xn xn xn ti t1 L : Lagrangian ti t1 xi xi xi x1 x1 x1 xi x1 S N'

  10. Path Integral Quantization cf. coordinate eigenstate fields completeness provability amplitude tn tn xn xn xn xn ti t1 ti t1 xi xi xi x1 x1 x1 xi x1 S N' : Lagrangian density

  11. operator fxj eigenvalue fxj f(x) : Lagrangian density

  12. fxj eigenvalue fxj f(x)

  13. fx a fx b fx fx a b f(xa)f(xb)

  14. fx a fx b fx fx a b f(xa)f(xb)

  15. generating functional +fJ functional derivative cf. partial derivative +fJ +fJ +fJ +fJ +fJ f (x) d(x-y) f (y) h

  16. +fJ +fJ +fJ +fJ f (y)

  17. +fJ +fJ f (y)

  18. commuting c-数 anti-commuting c-数 (Grassman数) 微分 積分

  19. cf

  20. scalarfとfermionyの系 generating functional

  21. gauge theory gauge boson とfermionyの系 generating functional is inappropriate because and does not have inverse. need gauge fixing

  22. gauge fixing

  23. =1 Faddeev Popov ghost

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