Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

• it’s instructive to prove at least one of the trace theorems yourselves, because ithelps to memorize the result.Problem 13. Computeusing the cyclic invariance of the tracetr (/a/b/c/d) (133)and subsequently the anti commutation relations (34).tr(ABC) = tr(BCA) (134)Problem 14. Compute the trace L µν (p, q, m) = tr [(/p + m)γ µ (/q − m)γ ν ].Problem 15. Compute L ρ2 ρ 1(p 1 , p 2 , 0)L ρ 1ρ 2(q1 , q 2 , 0) as a function of the Mandelstam variablesin the high energy limit s, −t, −u ≫ m 2 i .4.3 Cross SectionProblem 16. Compute the differential cross sectionfor e + e − → µ + µ − in the region s, −t, −u ≫ m 2 e.Problem 17. Compute the integrated cross sectionfor e + e − → µ + µ − in the region s ≫ m 2 e.dσdΩ (cos θ, E CM) (135)σ(E CM ) (136)4.4 FORM• very efficient computation using programs for symbolic manipulation, e. g. FORM.• declare variables1: vector p1, p2, q1, q2;2: symbol s, t, u, me, mq;3: indices rho1, rho2;• expressions4: local [TT*] =5: (g_(1, p2) - me*g_(1)) * g_(1, rho1)6: * (g_(1, p1) + me*g_(1)) * g_(1, rho2)7: * (g_(2, q1) + mq*g_(2)) * g_(2, rho1)8: * (g_(2, q2) - mq*g_(2)) * g_(2, rho2);26