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

pqp\cdot q

p0q0pqp^0 q^0-p\cdot q

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

ϵˉμνpq\bar{\epsilon }^{\mu \nu \overline{p}\overline{q}}

gˉ0μgˉ$MU($20)ν(ϵˉ$MU($20)pq)gˉ$MU($20)μ(gˉ0ν(ϵˉ$MU($20)pq)gˉ$MU($21)ν(q0ϵˉ$MU($20)$MU($21)pp0ϵˉ$MU($20)$MU($21)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 
  
 

γμ\gamma ^{\mu }

γˉ0gˉ0μγ$MU($22)g$MU($22)μ\bar{\gamma }^0 \bar{g}^{0\mu }-\gamma ^{\text{\$MU}(\text{\$22})} g^{\text{\$MU}(\text{\$22})\mu }