Feynman Diagrams For Pedestrians - Herbstschule Maria Laach

• traces9: trace4, 1;10: trace4, 2;11: print;12: .sort;• reduction to Mandelstam variables (114)s = (p 1 + p 2 ) 2 = 2m 2 e + 2p 1 p 2t = (q 2 − p 1 ) 2 = m 2 q + m 2 e − 2q 2 p 1(137a)(137b)etc.13: id p1.p2 = 1/2 * (s - 2*me^2);14: id q1.q2 = 1/2 * (s - 2*mq^2);15: id p1.q1 = - 1/2 * (t - me^2 - mq^2);16: id p2.q2 = - 1/2 * (t - me^2 - mq^2);17: id p1.q2 = - 1/2 * (u - me^2 - mq^2);18: id p2.q1 = - 1/2 * (u - me^2 - mq^2);• human intelligence (i. e. experience, cf. (211)): the result can be written mostcompactly as a function of t und u:19: id s = - u - t + 2*me^2 + 2*mq^2;20: bracket me, mq;21: print;22: .sort;running the program:ohl@thopad2:~fdfp$ form mumu.frmFORM by J.Vermaseren,version 3.3(Mar 28 2009) Run at: Thu Jul 7 18:37:42 2011[TT*] =64*me^2*mq^2 + 32*p1.p2*mq^2 + 32*p1.q1*p2.q2 + 32*p1.q2*p2.q1 + 32*q1.q2*me^2;[TT*] =+ mq^2 * ( - 32*u - 32*t )+ mq^4 * ( 48 )+ me^2 * ( - 32*u - 32*t )+ me^2*mq^2 * ( 96 )+ me^4 * ( 48 )+ 8*u^2 + 8*t^2;0.00 sec out of 0.00 sec27