-- www.eigenmath.org/muon-decay-1.txt -- Verify Casimir trick for muon decay. -- Requires about a minute to run. E1 = sqrt(p1x^2 + p1y^2 + p1z^2 + m1^2) E2 = sqrt(p2x^2 + p2y^2 + p2z^2 + m2^2) E3 = sqrt(p3x^2 + p3y^2 + p3z^2 + m3^2) E4 = sqrt(p4x^2 + p4y^2 + p4z^2 + m4^2) p1 = (E1, p1x, p1y, p1z) p2 = (E2, p2x, p2y, p2z) p3 = (E3, p3x, p3y, p3z) p4 = (E4, p4x, p4y, p4z) u11 = (E1 + m1, 0, p1z, p1x + i p1y) u12 = (0, E1 + m1, p1x - i p1y, -p1z) u21 = (E2 + m2, 0, p2z, p2x + i p2y) u22 = (0, E2 + m2, p2x - i p2y, -p2z) v31 = (p3z, p3x + i p3y, E3 + m3, 0) v32 = (p3x - i p3y, -p3z, 0, E3 + m3) u41 = (E4 + m4, 0, p4z, p4x + i p4y) u42 = (0, E4 + m4, p4x - i p4y, -p4z) u1 = (u11,u12) u2 = (u21,u22) v3 = (v31,v32) u4 = (u41,u42) I = ((1,0,0,0),(0,1,0,0),(0,0,1,0),(0,0,0,1)) gmunu = ((1,0,0,0),(0,-1,0,0),(0,0,-1,0),(0,0,0,-1)) gamma0 = ((1,0,0,0),(0,1,0,0),(0,0,-1,0),(0,0,0,-1)) gamma1 = ((0,0,0,1),(0,0,1,0),(0,-1,0,0),(-1,0,0,0)) gamma2 = ((0,0,0,-i),(0,0,i,0),(0,i,0,0),(-i,0,0,0)) gamma3 = ((0,0,1,0),(0,0,0,-1),(-1,0,0,0),(0,1,0,0)) gamma5 = i dot(gamma0,gamma1,gamma2,gamma3) gamma = (gamma0,gamma1,gamma2,gamma3) gammaT = transpose(gamma) gammaL = transpose(dot(gmunu,gamma)) pslash1 = dot(p1,gmunu,gamma) pslash2 = dot(p2,gmunu,gamma) pslash3 = dot(p3,gmunu,gamma) pslash4 = dot(p4,gmunu,gamma) u2bar = dot(conj(u2),gamma0) -- adjoint of u2 u4bar = dot(conj(u4),gamma0) -- adjoint of u4 -- S is the sum over spin states S = 0 for(s1,1,2,for(s2,1,2,for(s3,1,2,for(s4,1,2, X21 = dot(u2bar[s2],gammaT,I-gamma5,u1[s1]), X43 = dot(u4bar[s4],gammaL,I-gamma5,v3[s3]), M = dot(X43,X21), S = S + M conj(M) )))) -- T1 is the first trace matrix T1 = contract(dot(pslash4,gammaT,I - gamma5,pslash3,gammaT,I - gamma5),1,4) -- T2 is the second trace matrix T2 = contract(dot(pslash2,gammaL,I - gamma5,pslash1,gammaL,I - gamma5),1,4) -- T is the product of T1 and T2 T = contract(dot(T1,transpose(T2))) -- N is the normalization constant N = (E1 + m1) (E2 + m2) (E3 + m3) (E4 + m4) -- print 1 if equal S == N T