FermionSpinSum
FermionSpinSum[exp]
converts products of closed spinor chains in exp
into Dirac traces. Both Dirac and Majorana particles are supported. It is understood, that exp
represents a squared amplitude.
See also
Overview, Spinor, ComplexConjugate, DiracTrace.
Examples
FeynCalc uses the customary relativistic normalization of the spinors.
SpinorUBar[Momentum[p], m] . SpinorU[Momentum[p], m]
FermionSpinSum[%]
DiracSimplify[%]
uˉ(p,m).u(p,m)
tr(γˉ⋅p+m)
4m
SpinorVBar[Momentum[p], m] . SpinorV[Momentum[p], m]
FermionSpinSum[%]
DiracSimplify[%]
vˉ(p,m).v(p,m)
tr(γˉ⋅p−m)
−4m
amp = SpinorUBar[k1, m] . GS[p] . GA[5] . SpinorU[p1, m]
ampSq = amp ComplexConjugate[amp]
uˉ(k1,m).(γˉ⋅p).γˉ5.u(p1,m)
uˉ(k1,m).(γˉ⋅p).γˉ5.u(p1,m)(−(φ(p1,m)).γˉ5.(γˉ⋅p).(φ(k1,m)))
FermionSpinSum[ampSq]
DiracSimplify[%]
−tr((γˉ⋅k1+m).(γˉ⋅p).γˉ5.(γˉ⋅p1+m).γˉ5.(γˉ⋅p))
−4p2(k1⋅p1)+8(k1⋅p)(p⋅p1)−4m2p2