9 isospin in strong interacbons review we learned

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Unformatted text preview: denotes an adjoint spinor, not an anBparBcle). 2 Note that ( ( )) ⎛ 1− γ 5 ⎞ 1 = 1 − 2γ 5 + γ 5 ⎜2⎟ 4 ⎝ ⎠ ⎛1 − γ 5 ⎞ ⎛1 + γ 5 ⎞ γµ⎜ ⎟=⎜ ⎟γ µ 2⎠⎝2⎠ ⎝ 2 ⎛ 1− γ 5 ⎞ =⎜ ⎟ ⎝2⎠ since (γ ) 52 =1 ⎛1 − γ 5 ⎞ MulBply by ⎜ ⎟ on the RHS of each side of this expression 2⎠ ⎝ ⎛ 1 − γ 5 ⎞⎛1 − γ 5 ⎞ ⎛1 + γ 5 ⎞ ⎛1 − γ 5 ⎞ ⎛1 − γ 5 ⎞ ⎛1 + γ 5 ⎞ ⎛1 − γ 5 ⎞ γµ⎜ ⎟⎜ ⎟=⎜ ⎟γ µ ⎜ ⎟ ⇒ γµ⎜ ⎟=⎜ ⎟γ µ ⎜ ⎟ So we can write ⎝ 2 ⎠⎝ 2 ⎠ ⎝ 2 ⎠ ⎝ 2 ⎠ ⎝2⎠⎝2⎠⎝2⎠ 7 ⎛ 1− γ 5 ⎞ ⎛ 1+ γ 5 ⎞ ⎛ 1− γ 5 ⎞ So we can write j = νγ µ ⎜ ⎟ e = ν ⎜ 2 ⎟ γ µ ⎜ 2 ⎟ e = ν Lγ µ eL ⎝2⎠ ⎝ ⎠⎝ ⎠ − µ Since the notaBon might be confusing, I remind you that this represents an adjoint parBcle spinor for the neutrino. And the (cha...
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