Since version 9.3 FeynCalc can also deal with manifestly noncovariant expressions, such as 3-vectors, Kronecker deltas and Pauli matrices
CV[p, i]\overline{p}^i
CV[p, i] CV[q, i]
% // Contract\overline{p}^i \overline{q}^i
\overline{p}\cdot \overline{q}
CLC[i, j, k] CLC[i, j, l]
% // Contract\bar{\epsilon }^{ijk} \bar{\epsilon }^{ijl}
2 \bar{\delta }^{kl}
CSI[i, j, i]
% // PauliSimplify\overline{\sigma }^i.\overline{\sigma }^j.\overline{\sigma }^i
-\overline{\sigma }^j
PauliTrace[CSI[i, j, i, j]]
% // PauliSimplify\text{tr}\left(\overline{\sigma }^i.\overline{\sigma }^j.\overline{\sigma }^i.\overline{\sigma }^j\right)
-6
The function LorentzToCartesian is used to break the manifest Lorentz covariance when doing nonrelativistic expansions
SP[p, q]
% // LorentzToCartesian\overline{p}\cdot \overline{q}
p^0 q^0-\overline{p}\cdot \overline{q}