SpinorChainTranspose[exp] transposes particular spinor
chains in exp, which effectively switches the u and v
spinors and reverses the order of the Dirac matrices using charge
conjugation operator. This operation is often required in calculations
that involve Majorana particles. By default, the function will tranpose
all chains of the form \bar{v}.x.u and
\bar{v}.x.v. A different or more fine
grained choice can be obtained via the option Select.
Overview, FCChargeConjugateTransposed, DiracGamma, Spinor.
SpinorVBarD[p1, m1] . GAD[\[Mu]] . (GSD[p] + m) . GAD[\[Mu]] . SpinorUD[p2, m2]
SpinorChainTranspose[%]\bar{v}(\text{p1},\text{m1}).\gamma ^{\mu }.(m+\gamma \cdot p).\gamma ^{\mu }.u(\text{p2},\text{m2})
-(\varphi (-\text{p2},\text{m2})).\gamma ^{\mu }.(m-\gamma \cdot p).\gamma ^{\mu }.(\varphi (\text{p1},\text{m1}))
SpinorUBarD[p1, m1] . GAD[\[Mu]] . (GSD[p] + m) . GAD[\[Mu]] . SpinorVD[p2, m2]
SpinorChainTranspose[%]\bar{u}(\text{p1},\text{m1}).\gamma ^{\mu }.(m+\gamma \cdot p).\gamma ^{\mu }.v(\text{p2},\text{m2})
(\varphi (\text{p1},\text{m1})).\gamma ^{\mu }.(m+\gamma \cdot p).\gamma ^{\mu }.(\varphi (-\text{p2},\text{m2}))
SpinorUBarD[p1, m1] . GAD[\[Mu]] . (GSD[p] + m) . GAD[\[Mu]] . SpinorVD[p2, m2]
SpinorChainTranspose[%, Select -> {{SpinorUBarD[_, _], SpinorVD[_, _]}}]\bar{u}(\text{p1},\text{m1}).\gamma ^{\mu }.(m+\gamma \cdot p).\gamma ^{\mu }.v(\text{p2},\text{m2})
-(\varphi (\text{p2},\text{m2})).\gamma ^{\mu }.(m-\gamma \cdot p).\gamma ^{\mu }.(\varphi (-\text{p1},\text{m1}))