FeynCalc manual (development version)

SpinorChainTrick

SpinorChainTrick[exp] applies several simplifications to products of spinor chains.

See also

Overview, FCCanonicalizeDummyIndices, DiracGamma, Spinor.

Examples

a SpinorUBar[p1, m1] . GA[\[Mu]] . SpinorU[p2, m2] SpinorVBar[p1, m1] . GA[\[Mu]] . SpinorV[p4, m4] +
   b SpinorUBar[p1, m1] . GA[\[Nu]] . SpinorU[p2, m2] SpinorVBar[p1, m1] . GA[\[Nu]] . SpinorV[p4, m4] 
 
SpinorChainTrick[%]

a \bar{u}(\text{p1},\text{m1}).\bar{\gamma }^{\mu }.u(\text{p2},\text{m2}) \bar{v}(\text{p1},\text{m1}).\bar{\gamma }^{\mu }.v(\text{p4},\text{m4})+b \bar{u}(\text{p1},\text{m1}).\bar{\gamma }^{\nu }.u(\text{p2},\text{m2}) \bar{v}(\text{p1},\text{m1}).\bar{\gamma }^{\nu }.v(\text{p4},\text{m4})

(a+b) \left(\varphi (\overline{\text{p1}},\text{m1})\right).\bar{\gamma }^{\text{FCGV}(\text{LI191})}.\left(\varphi (\overline{\text{p2}},\text{m2})\right) \left(\varphi (-\overline{\text{p1}},\text{m1})\right).\bar{\gamma }^{\text{FCGV}(\text{LI191})}.\left(\varphi (-\overline{\text{p4}},\text{m4})\right)

SpinorUBar[p1, m1] . GAE[\[Mu]] . SpinorU[p2, m2] SpinorVBar[p1, m1] . GA[\[Mu]] . SpinorV[p4, m4] 
 
SpinorChainTrick[%]

\bar{u}(\text{p1},\text{m1}).\hat{\gamma }^{\mu }.u(\text{p2},\text{m2}) \bar{v}(\text{p1},\text{m1}).\bar{\gamma }^{\mu }.v(\text{p4},\text{m4})

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