FeynCalc manual (development version)

FieldStrength

FieldStrength[mu, nu, a] is the field strength tensor μAνaνAμa+gsAμbAνcfabc\partial _{\mu } A_{\nu }^a - \partial _{\nu } A_{\mu }^a + g_s A_{\mu }^b A_{\nu }^c f^{abc}.

FieldStrength[mu, nu] is the field strength tensor (μAννAμ)(\partial _{\mu } A_{\nu}- \partial_{\nu } A_{\mu}).

The name of the field (AA) and the coupling constant (gg) can be set through the options or by additional arguments. The first two indices are interpreted as type LorentzIndex, except OPEDelta, which is converted to Momentum[OPEDelta].

See also

Overview

Examples

FieldStrength[\[Mu], \[Nu]]

FμνF_{\mu \nu }^{}

FieldStrength[\[Mu], \[Nu], a]

FμνaF_{\mu \nu }^a

FieldStrength[\[Mu], \[Nu], Explicit -> True]

(μAν)(νAμ)\left.(\partial _{\mu }A_{\nu }\right)-\left.(\partial _{\nu }A_{\mu }\right)

FieldStrength[\[Mu], \[Nu], a, Explicit -> True]

gsfab19  c20Aμb19.Aνc20+(μAνa)(νAμa)g_s f^{a\text{b19}\;\text{c20}} A_{\mu }^{\text{b19}}.A_{\nu }^{\text{c20}}+\left.(\partial _{\mu }A_{\nu }^a\right)-\left.(\partial _{\nu }A_{\mu }^a\right)

FieldStrength[\[Mu], \[Nu], a, CouplingConstant -> -SMP["g_s"], Explicit -> True]

gsfab21  c22Aμb21.Aνc22+(μAνa)(νAμa)-g_s f^{a\text{b21}\;\text{c22}} A_{\mu }^{\text{b21}}.A_{\nu }^{\text{c22}}+\left.(\partial _{\mu }A_{\nu }^a\right)-\left.(\partial _{\nu }A_{\mu }^a\right)