1. 前回のSummary
Path Integral Quantization
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
example 　　　
SU(3)=group of complex 3×3 matrices U
withUU †=1 (unitary) & det U = 1 (special)
generator
li Gell-mann matrices
commutators
f ijkは完全反対称
irreducible representations
are specified by two integers 1 2 3 6 10 3* 8 15 6*
15* 27
10*
......

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

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

6. gauge fixing xi = = yj

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

9. Grassman number
Faddeev Popov ghost

10. fermionも加える
Lagrangian

11. fermionも加える
Lagrangian