Traces of two, three, four Dirac matrix products.

<<DiracWeyl`;

g[mu_] := Superscript["γ", mu];
g[5] := Subscript["γ", 5];
Table[Row[{g[i], " = ",(DiracMatrix[i]// MatrixForm), ", "}],{i,0,5}] // Row
Table[Row[{g[i], g[j], " = ", DiracMatrix[i].DiracMatrix[j]// MatrixForm}],{i,0,3},{j,0,3}] // Grid
Row[{"\!\(\*SuperscriptBox[\(γ\), \(\(0\)\(\\ \)\)]\)\!\(\*SuperscriptBox[\(γ\), \(\(1\)\(\\ \)\)]\)\!\(\*SuperscriptBox[\(γ\), \(\(2\)\(\\ \)\)]\)\!\(\*SuperscriptBox[\(γ\), \(\(3\)\(\\ \)\)]\)= ", DiracMatrix[0].DiracMatrix[1].DiracMatrix[2].DiracMatrix[3]// MatrixForm}]
Table[Row[{"tr( ", g[i], g[j], ") = ", Tr[DiracMatrix[i].DiracMatrix[j]]}],{i,0,3},{j,0,3}] // Grid

Table[Row[{"tr( ", g[i], g[j], g[k], g[l], ") = ", Tr[DiracMatrix[i].DiracMatrix[j].DiracMatrix[k].DiracMatrix[l]], ", "}],{i,0,3},{j,0,3},{k,0,3},{l,0,3}] // Grid

(*Table[Row[{"tr( γ[", i, "] γ[", j, "] γ[", k, "]) = ", Tr[DiracMatrix[i].DiracMatrix[j].DiracMatrix[k]]}],{i,0,3},{j,0,3}, {k,0,3}] // Flatten// Column*)
(*

Table[ Tr[DiracMatrix[i].DiracMatrix[j].DiracMatrix[k]],{i,0,3},{j,0,3}, {k,0,3}] // Flatten
*)