FeynCalc manual (development version)

Spinor

Spinor[p, m, o] is the head of Dirac spinors. Which of the spinors u, v, \bar{u} or \bar{v} is understood, depends on the sign of the momentum argument p and the relative position of Spinor in the chain.

Spinors of fermions of mass m are normalized to have \bar{u} u=2 m and \bar{v} v=-2 m.

The optional argument o can be used for additional degrees of freedom. If no optional argument o is supplied, a 1 is substituted in.

See also

Overview, FermionSpinSum, DiracSimplify, SpinorU, SpinorV, SpinorUBar, SpinorVBar, SpinorUBarD, SpinorUD, SpinorVD, SpinorVBarD.

Examples

Spinor[Momentum[p]]

\varphi (\overline{p})

Spinor[Momentum[p], m]

\varphi (\overline{p},m)

FeynCalc uses covariant normalization (as opposed to e.g. the normalization used in Bjorken & Drell).

Spinor[Momentum[p], m] . Spinor[Momentum[p], m] // DiracSimplify

2 m

DiracSimplify[Spinor[-Momentum[p], m] . GS[p]]

-m \left(\varphi (-\overline{p},m)\right)

Spinor[Momentum[p]] // StandardForm

(*Spinor[Momentum[p], 0, 1]*)
ChangeDimension[Spinor[Momentum[p]], D] // StandardForm

(*Spinor[Momentum[p, D], 0, 1]*)
Spinor[Momentum[p], m] // StandardForm

(*Spinor[Momentum[p], m, 1]*)

SmallVariables are discarded by Spinor.

Spinor[Momentum[p], SmallVariable[m]] // StandardForm

(*Spinor[Momentum[p], 0, 1]*)