Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

• compare1p 2 − m 2 +iɛ = 1(p 0 ) 2 − (|⃗p| 2 + m 2 ) +iɛE>0=1(p 0 ) 2 − (E−iɛ) = 12 p 0 − E+iɛImp 0Rep 0− √ |⃗p| 2 + m 2 + √ |⃗p| 2 + m 2√E=+ |⃗p| 2 +m 2=1p 0 + E−iɛ = 12E1(p 0 ) 2 − E 2 +iɛ(1p 0 − E+iɛ − 1)p 0 + E−iɛ(96)• forward in time:x 0 > 0 :limp 0 →−i∞ e−ip 0x 0→ 0the integration contour in (94) can be closed below(97a)Imp 0Rep 0• backward in time:x 0 < 0 :limp 0 →+i∞ e−ip 0x 0→ 0the integration contour in (94) can be closed above(97b)Imp 0Rep 0∴ inΦ ′ (x) =∫∫ dd 4 4 p1y D(x − y, m)Φ(y) =(2π) 4 e−ipx p 2 − m 2 +iɛ ˜Φ(p) (98)• the part of ˜Φ(p) with p 0 = + √ |⃗p| 2 + m 2 is propagated into the future• the part of ˜Φ(p) with p 0 = − √ |⃗p| 2 + m 2 is propagated into the past• Compton scattering in nonrelativistic perturbation theory contains scattering aswell as pair creation and pair annihilation contributions:t 1 t 2 +t1t 2+18t 1+t 2t 1(99)t 2