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前回の Summary

Path Integral Quantization. 前回の Summary. path Integral. generating functional. Gauge Theory. for gauge field & spinor field. Assume Lorentz inv., locality, superficial renormalizability & . local gauge symmetry. with Lie group G. Lie algebra g. gauge transformation.

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前回の Summary

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  1. Path Integral Quantization 前回のSummary path Integral generating functional

  2. Gauge Theory for gauge field & spinor field Assume Lorentz inv., locality, superficial renormalizability & local gauge symmetry with Lie group G. Lie algebra g. gauge transformation b i:parameter, depends on xm Xi: generator of G f ijk: structure constants of G T i: representation of Xi on y Lagrangian field strength covariant derivative

  3. SU(3)=group of complex 3×3 matrices U withUU†=1 (unitary) & detU = 1 (special) example generator li Gell-mann matrices f ijkは完全反対称 commutators irreducible representations are specified by two integers

  4. Path intdegral quantization of gauge theories としてみる =0 ∂mKmn =-∂n∂2+∂2∂n generating functional ∂m is inappropriate ∵ does not exist. ∂m = = ∂l 0 need gauge fixing 矛盾 (K-1)mn we choose the gauge with does not exist.

  5. gauge fixing need gauge fixing we choose the gauge with

  6. gauge fixing xi = = yj

  7. gauge fixing = (gauge不変性より) i Gm = 無限大の定数 物理はBi によらない 無限大の定数 =

  8. Grassman number Faddeev Popov ghost

  9. fermionも加える Lagrangian

  10. fermionも加える Lagrangian

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