B we have been discussing things in terms of

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Unformatted text preview: That is, these are eigenstates of 3 with eigenvalues ± 1/2. Expect eigenvalues of τ 2 ≡ τ ⋅ τ to then be ½(½+1) = ¾. Check this: ⎡1 ⎛ 1 0 ⎞⎤ 3 τ χ =τ +τ +τ = 3 ⎢ ⎜ χ= χ ⎟⎥ 4 ⎢4 ⎝ 0 1 ⎠⎥ ⎣ ⎦ 2 2 1 2 2 2 3 ✔ Can make isospin raising or lowering operators τ ± = ( τ 1 ± i τ ) 2 ⎛0 1⎞ τ =⎜ ⎟ 0 0⎠ ⎝ + ⎛ 0 0⎞ τ =⎜ ⎟ 1 0⎠ ⎝ − Applying these operators to the two states, we see τ+ p = 0 τ+ n = p τ− p = n τ− n = 0 11 Back to the weak interacBon.…… We we have (so far) − j µ = ν L γ µ eL + j µ = eL γ µν L ⎫ ⎪ ⎪ ⎬ ⎪ ⎪ ⎭ charged weak currents em j µ = −e γ µ e = −eL γ µ eL − eR γ µ eR EM current (neutral) 12 Neutral Weak Currents We have expressions for the “posiBve” and “negaBve” weak charged current: νe νe e − jµ = ν Lγ µ eL Weak-isospin lowering W + jµ = eLγ µν L Weak-isospin raising e W ⎛ν e ⎞ Can write this compactly by defining the le] ­hande...
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This document was uploaded on 02/11/2014.

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