Feynman Diagrams For Pedestrians - Herbstschule Maria Laach
Feynman Diagrams For Pedestrians - Herbstschule Maria Laach
Feynman Diagrams For Pedestrians - Herbstschule Maria Laach
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Therefore2∑k=12∑k=1u k (p)ū k (p) = (/p + m) (γ 0 + 1) (/p + m)2(p 0 + m)v k (p)¯v k (p) = (/p − m) (γ 0 − 1) (/p − m)2(p 0 + m)(195a)(195b)and (60) follows from(/p ± m)(γ 0 ± 1)(/p ± m) = /pγ 0 /p ± (mγ 0 /p + m/pγ 0 ) + m 2 γ 0 ± (/p ± m) 2= −p 2 γ 0 + 2p 0 /p ± 2p 0 m + m 2 γ 0 + 2m(/p ± m) = 2(p 0 + m)(/p ± m) . (196)Solution 5.ū k (p)u l (p) = ū k ( ⃗ 0)/p + m√p0 + m/p + m√p0 + m u l( ⃗ 0)= 2mp 0 + mūk( ⃗ 0)(/p + m)u l ( ⃗ 0)= 2mp 0 + mūk( ⃗ 0)(p 0 + m)u l ( ⃗ 0) = 2mū k ( ⃗ 0)u l ( ⃗ 0) = 2mδ kl (197)¯v k (p)v l (p) = ¯v k ( ⃗ 0)/p − m√p0 + m/p − m√p0 + m v l( ⃗ 0)= −2mp 0 + m ¯v k( ⃗ 0)(/p − m)v l ( ⃗ 0)= 2mp 0 + m ¯v k( ⃗ 0)(p 0 + m)v l ( ⃗ 0) = 2m¯v k ( ⃗ 0)v l ( ⃗ 0) = −2m · δ kl (198)ū k (p)v l (p) = ū k ( ⃗ 0)¯v k (p)u l (p) = ¯v k ( ⃗ 0)/p + m√p0 + m/p − m√p0 + m/p − m√p0 + m v l( ⃗ 0) = 0/p + m√p0 + m u l( ⃗ 0) = 0(199a)(199b)40