Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

∵ intermediate states violate energy conservation and vertices can have space likedistances∴ temporal order of t 1 and t 2 depends in general on the reference frame, i. e. isundefined• Feynman’s brilliant (re-)interpretation:– particles with p 0 = + √ |⃗p| 2 + m 2 are propagated into the future– anti particles with p 0 = − √ |⃗p| 2 + m 2 and opposite charges are propagatedinto past∴ charges are conserved along the arrows in (99)!∴ the four nonrelativistic diagrams in (99) can be combined to two covariantexpressions using Feynman propagatorst 1 t 2 +11E−E 0 +iɛ E+E 0 +iɛt 1=t 21p 2 − m 2 +iɛ(100a)1E−E 0 +iɛt 1t 2+1E+E 0 +iɛt 1=t 21p 2 − m 2 +iɛ(100b)∴ the Feynman propagator allows to extend our interpretation of external, noninteractinganti particles as particles traveling backward in time to interactingparticles.Problem 12. Compute the propagator S(x, m) for Dirac particles in momentum space!• propagator for massless spin-1 particles−ig µν + i(1 − ξ) k µk νk 2 +iɛk 2 + iɛ(101)• the gauge parameter ξ ist arbitrary and must cancel in the final result• partial results can depend on ξ• the propagator for massive spin-1 particles−ig µν + i k µk νM 2k 2 − M 2 + iɛis not gauge dependent, because (76 ′ ) can be inverted, contrary to (73 ′ )(102)19