Gell-Mann matrices Definition

λ1={{0,1,0},{1,0,0},{0,0,0}};
λ2={{0,-I,0},{I,0,0},{0,0,0}};
λ3={{1,0,0},{0,-1,0},{0,0,0}};
λ4={{0,0,1},{0,0,0},{1,0,0}};
λ5={{0,0,-I},{0,0,0},{I,0,0}};
λ6={{0,0,0},{0,0,1},{0,1,0}};
λ7={{0,0,0},{0,0,-I},{0,I,0}};
λ8=(1/(√3)){{1,0,0},{0,1,0},{0,0,-2}};
λ={λ1,λ2,λ3,λ4,λ5,λ6,λ7,λ8}; 
T=(1/2)λ;(* esta es la normalizacion para que ahora sean los generadores de SU(3) que van en los vertices de QCD *)
For[i=1,i≤8,i++,Print["T[",i,"]=",T[[i]]//MatrixForm]]

Trace property: Tr[(T^a)(T^b)]=(1/2)(δ^ab)

out=Array[x,{8,8}];
For[a=1,a≤8,a++,
For[b=1,b≤8,b++,
out[[a,b]]=Tr[T[[a]].T[[b]]];
]
]
out

casimir operators

(* this is the obvious Casimir operator, proportional to identity *)
c1=Sum[T[[a]].T[[a]],{a,1,8}]

(* This comes from: http://thespectrumofriemannium.wordpress.com/tag/casimir-operators-for-su3/ *)
c2=(1/(√3))T[[1]].T[[1]].T[[8]]+
(1/2)T[[1]].T[[4]].T[[6]]+
(1/2)T[[1]].T[[5]].T[[7]]+
(1/(√3))T[[2]].T[[2]].T[[8]]+
((-1)/2)T[[2]].T[[4]].T[[7]]+
(1/2)T[[2]].T[[5]].T[[6]]+
(1/(√3))T[[3]].T[[3]].T[[8]]+
(1/2)T[[3]].T[[4]].T[[4]]+
(1/2)T[[3]].T[[5]].T[[5]]+
((-1)/2)T[[3]].T[[6]].T[[6]]+
((-1)/2)T[[3]].T[[7]].T[[7]]+
((-1)/(2√3))T[[4]].T[[4]].T[[8]]+
((-1)/(2√3))T[[5]].T[[5]].T[[8]]+
((-1)/(2√3))T[[6]].T[[6]].T[[8]]+
((-1)/(2√3))T[[7]].T[[7]].T[[8]]+
((-1)/(√3))T[[8]].T[[8]].T[[8]]

For[a=1,a≤8,a++,Print[c2.T[[a]]-T[[a]].c2]]