FeynRule

Description

FeynRule[lag, {fields}] derives the Feynman rule corresponding to the field configuration fields of the lagrangian lag.

Options[FeynRule]

FeynRule does not calculate propagator Feynman rules.

The option ZeroMomentumInsertion can be used for twist-2 and higher twist operators.

See also:  Lagrangian.

Examples

gou = Lagrangian["ogu"]

gop = Lagrangian["ogp"]

Explicit[gop]

Cases2[%, QuantumField]

2-gluon Feynman rules (unpolarized)

fi = {QuantumField[GaugeField, {μ}, {a}][
          p], QuantumField[GaugeField, {ν}, {b}][q]}

f2u = 
      FullSimplify /@ 
        Factor2[FeynRule[gou, fi, 
            ZeroMomentumInsertion -> False]]

2-gluon Feynman rules (polarized)

fi = {QuantumField[GaugeField, {μ}, {a}][
          p], QuantumField[GaugeField, {ν}, {b}][q]}

f2p = 
      FullSimplify /@ 
        Factor2[FeynRule[gop, fi, 
            ZeroMomentumInsertion -> False]]

Factor2[Calc[f2p /. p -> -q]]

Compare with the Feynman rule tabulated in Twist2GluonOperator.

Twist2GluonOperator[q, {μ, a}, {ν, b}, Polarization -> 1, 
      Explicit -> True]

quark-quark Feynman rule (unpolarized)

qo = Lagrangian["oqu"]

quark-quark -gluon-gluon Feynman rule (unpolarized)

qo = Lagrangian["oqu"]

qggf = {QuantumField[QuarkField][
          p], QuantumField[AntiQuarkField][
          q], QuantumField[GaugeField, {μ}, {a}][
          r], QuantumField[GaugeField, {ν}, {b}][s]}

n4 = FeynRule[qo, qggf, ZeroMomentumInsertion -> True]

t4 = 
      Twist2QuarkOperator[{p}, {q}, {r, μ, a}, {s, ν, b}, 
        Polarization -> 0]

Calc[n4 - t4 /. OPEm -> 5 /. s -> -p - q - r /. 
        D -> 4]

In general equality can be shown by Timing[Factor2[ FCE[Calc[ChangeDimension[FCE[OPESumExplicit[n4-t4]],4]/.s->-p-q-r]]]] but it is a little bit slow ...

Clear[qggf, n2, n4]

QCD vertices

fii = {QuantumField[GaugeField, {μ}, {a}][
          p], QuantumField[GaugeField, {ν}, {b}][
          q], QuantumField[GaugeField, {ρ}, {c}][r]}

g3 = FeynRule[Lagrangian["QCD"], fii]

GluonVertex[{p, μ, a}, {q, ν, b}, {r, ρ, c}, 
      Explicit -> True]

Calc[g3 - ChangeDimension[%, 4]]

fi4 = {QuantumField[GaugeField, {μ}, {a}][
          p], QuantumField[GaugeField, {ν}, {b}][
          q], QuantumField[GaugeField, {ρ}, {c}][
          r], QuantumField[GaugeField, {σ}, {d}][s]}

g4 = FeynRule[Lagrangian["QCD"], fi4]

GluonVertex[{p, μ, a}, {q, ν, b}, {r, ρ, c}, {s, σ, 
        d}, Explicit -> True]

Calc[g4 - ChangeDimension[%, 4]]

Clear[f2p, f2u, f3, f32, fi, fi4, fii, g3, g4, gop, gou, n3, nf3, n4, 
      np2, npf3, p33, pf3, pn3, pqo, qf, qp, qgf, qo, t4]