Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

4 QED• Quantum Electro Dynamics: interacting electrons, positrons and photons (andother charged particles)• single interaction vertex for fermions:pffk, µp ′ = iQ f eγ µ (120)with the electrical charge Q f of the particle, e. g. Q e = −1 for electrons• charged bosons require an additional (“sea gull”) vertexpsk, µk ′ , ν= iQ s e(p µ + p µ),′sp ′k, µ= 2iQ 2 se 2 g µν (121)4.1 e + e − → µ + µ − iT =¯v(p 2 )v(q 2 )−ieγ ρ−ig ρσ−ieγ σ (122)(p 1 + p 2 ) 2 + iɛu(p 1 )ū(q 1 )iT = ¯v(p 2 )(−ieγ ρ −ig ρσ)u(p 1 )(p 1 + p 2 ) 2 + iɛū(q 1)(−ieγ σ )v(q 2 )∑spinsTT † = e2s= i e2s [¯v(p 2)γ ρ u(p 1 )] [ū(q 1 )γ ρ v(q 2 )] (123)e 2s [¯v(p 2)γ ρ1 u(p 1 )ū(p 1 )γ ρ2 v(p 2 )] [ū(q 1 )γ ρ 1v(q 2 )¯v(q 2 )γ ρ 2u(q 1 )]TT † = e4s 2 tr [(/p 2 − m e )γ ρ1 (/p 1 + m e )γ ρ2 ]tr [(/q 1 + m µ )γ ρ 1(/q 2 − m µ )γ ρ 2](124)= e4s 2 L ρ 2 ρ 1(p 1 , p 2 , m e )L ρ 1ρ 2(q 1 , q 2 , m µ ) (125)24