LorentzToCartesian[exp]
rewrites Lorentz tensors in form
of Cartesian tensors (when possible). Using options one can specify
which types of tensors should be converted.
[p, q]
SPD
% // LorentzToCartesian
p\cdot q
p^0 q^0-p\cdot q
[\[Mu], \[Nu]][p, q]
LC
% // LorentzToCartesian
\bar{\epsilon }^{\mu \nu \overline{p}\overline{q}}
\bar{g}^{0\mu } \bar{g}^{\text{\$MU}(\text{\$20})\nu } \left(-\bar{\epsilon }^{\text{\$MU}(\text{\$20})\overline{p}\overline{q}}\right)-\bar{g}^{\text{\$MU}(\text{\$20})\mu } \left(\bar{g}^{0\nu } \left(-\bar{\epsilon }^{\text{\$MU}(\text{\$20})\overline{p}\overline{q}}\right)-\bar{g}^{\text{\$MU}(\text{\$21})\nu } \left(q^0 \bar{\epsilon }^{\text{\$MU}(\text{\$20})\text{\$MU}(\text{\$21})\overline{p}}-p^0 \bar{\epsilon }^{\text{\$MU}(\text{\$20})\text{\$MU}(\text{\$21})\overline{q}}\right)\right)
[\[Mu]]
GAD
% // LorentzToCartesian
\gamma ^{\mu }
\bar{\gamma }^0 \bar{g}^{0\mu }-\gamma ^{\text{\$MU}(\text{\$22})} g^{\text{\$MU}(\text{\$22})\mu }