FeynCalc manual (development version)

LorentzToCartesian

LorentzToCartesian[exp] rewrites Lorentz tensors in form of Cartesian tensors (when possible). Using options one can specify which types of tensors should be converted.

See also

Overview, CartesianToLorentz.

Examples

SPD[p, q] 
 
% // LorentzToCartesian

p\cdot q

p^0 q^0-p\cdot q

LC[\[Mu], \[Nu]][p, q] 
 
% // 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)

GAD[\[Mu]] 
 
% // LorentzToCartesian 
  
 

\gamma ^{\mu }

\bar{\gamma }^0 \bar{g}^{0\mu }-\gamma ^{\text{\$MU}(\text{\$22})} g^{\text{\$MU}(\text{\$22})\mu }