# LeviCivitaTensor contraction indices

My computer has problems when I try to perform a calculation with TensorContract.

In particular, with the second answer to my previous question Contracting indices in lists, I want to compute (Einsten summation convention on repeated indices is used)

,

where we have the 4-dimensional Levi-Civita tensor, $$\gamma^\mu$$ are four 4x4 matrices defined by

Clear[γ]
SetAttributes[γ, Listable]
γ[μ_] := If[μ == 0, KroneckerProduct @@ PauliMatrix[{1, μ}], I KroneckerProduct @@ PauliMatrix[{2, μ}]]


and $$\psi^{\rho\sigma}$$ are a set of 16 4x1 matrices (i.e. vectors) defined by

Clear[ψ]
SetAttributes[ψ, Listable]
ψ[μ_, ν_] := If[μ == ν, {{0}, {0}, {0}, {0}}, {{psi0[μ, ν]}, {psi1[μ, ν]}, {psi2[μ, ν]}, {psi3[μ, ν]}}] ψμν = Outer[ψ, Range[0, 3], Range[0, 3]] // SparseArray


All the Greek indices run from 0 to 3. In particular, the expression I want to obtain has a free indices $$\mu$$, and so it is a 1-index tensor. To obtain the zeroth component ($$\mu=0$$, for example, I define

Clear[a]
SetAttributes[a, Listable]
a[μ_] := If[μ == 0, a[μ] = 1, a[μ] = 0]
aμ = a[Range[0, 3]]


so that

,

and use (see my previous question!) TensorContract[TensorProduct[LeviCivitaTensor[4], γμ, ψμν, η, η, η, aμ, η], {{1, 18}, {2, 11}, {3, 13}, {4, 15}, {5, 12}, {7, 10}, {8, 14}, {9, 16}, {17, 9}}].

My computer is just not able to do this: Mathematica crashes. Am I doing something wrong? Is there something I don't know about TensorContract, like a maximum number of arguments or stuff like that? If not, how can I solve this problem (changing computer is not an option)?