Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

• the interference terms are more complicated and contain traces of eight DiracmatricesT s T t ∗ = e 4 1 st [¯v(p 2)γ ρ1 u(p 1 )] [ū(p 1 )γ ρ 2u(q 1 )] [ū(q 1 )γ ρ 1v(q 2 )] [¯v(q 2 )γ ρ2 v(p 2 )]14: local [ST*] =15: (g_(1, p2) - me*g_(1)) * g_(1, rho1)16: * (g_(1, p1) + me*g_(1)) * g_(1, rho2)17: * (g_(1, q1) + me*g_(1)) * g_(1, rho1)18: * (g_(1, q2) - me*g_(1)) * g_(1, rho2);(142)T t T s ∗ = e 4 1 st [¯v(p 2)γ ρ1 v(q 2 )] [¯v(q 2 )γ ρ 2u(q 1 )] [ū(q 1 )γ ρ 1u(p 1 )] [ū(p 1 )γ ρ2 v(p 2 )]19: local [TS*] =20: (g_(1, p2) - me*g_(1)) * g_(1, rho1)21: * (g_(1, q2) - me*g_(1)) * g_(1, rho2)22: * (g_(1, q1) + me*g_(1)) * g_(1, rho1)23: * (g_(1, p1) + me*g_(1)) * g_(1, rho2);• FORM does the traces just the same . . .24: trace4, 1;25: trace4, 2;26: .sort;(143)• reduction to Mandelstam variables again as above, but all masses are equal27: id p1.p2 = 1/2 * (s - 2*me^2);28: id q1.q2 = 1/2 * (s - 2*me^2);29: id p1.q1 = - 1/2 * (t - 2*me^2);30: id p2.q2 = - 1/2 * (t - 2*me^2);31: id p1.q2 = - 1/2 * (u - 2*me^2);32: id p2.q1 = - 1/2 * (u - 2*me^2);• human intelligence and experience: the expression for |T s | 2 is most compact asfunction of t and u33: id s = - u - t + 4*me^2;34: bracket me;35: print;36: .sort;• the expression for |T t | 2 is most compact as function of s and u29