FeynCalc manual (development version)

QuantumField

QuantumField is the head of quantized fields and their derivatives.

QuantumField[par, ftype, {lorind}, {sunind}] denotes a quantum field of type ftype with (possible) Lorentz-indices lorind and SU(N) indices sunind. The optional first argument par denotes a partial derivative acting on the field.

See also

Overview, FeynRule, FCPartialD, ExpandPartialD.

Examples

This denotes a scalar field.

QuantumField[S]

S

Quark fields

QuantumField[AntiQuarkField]

\bar{\psi }

QuantumField[QuarkField]

\psi

This is a field with a Lorentz index.

QuantumField[B, {\[Mu]}]

B_{\mu }

Color indices should be put after the Lorentz ones.

QuantumField[GaugeField, {\[Mu]}, {a}] // StandardForm

(*QuantumField[GaugeField, LorentzIndex[\[Mu]], SUNIndex[a]]*)

A_{\Delta}^a is a short form for \Delta ^{mu } A_{mu }^a

QuantumField[A, {OPEDelta}, {a}]

A_{\Delta }^a

The first list of indices is usually interpreted as type LorentzIndex, except for OPEDelta, which gets converted to type Momentum.

QuantumField[A, {OPEDelta}, {a}] // StandardForm

(*QuantumField[A, Momentum[OPEDelta], SUNIndex[a]]*)

Derivatives of fields are denoted as follows.

QuantumField[FCPartialD[LorentzIndex[\[Mu]]], A, {\[Mu]}]

\left.(\partial _{\mu }A_{\mu }\right)

QuantumField[FCPartialD[OPEDelta], S]

\left.(\partial _{\Delta }S\right)

QuantumField[FCPartialD[OPEDelta], A, {OPEDelta}, {a}]

\left.(\partial _{\Delta }A_{\Delta }^a\right)

QuantumField[FCPartialD[OPEDelta]^OPEm, A, {OPEDelta}, {a}]

\partial _{\Delta }^m{}^{A\Delta a}

QuantumField[QuantumField[A]] === QuantumField[A]

\text{True}