FEYN CALC SYMBOL

# CovariantD

is a generic covariant derivative with Lorentz index mu. With the option-setting Explicit True, an explicit expression for a fermionic field is returned, depending on the setting on the other options. CovariantD[x, mu] is a generic covariant derivative with respect to x^mu. CovariantD[mu, a, b] is a covariant derivative for a bosonic field; acting on QuantumField[f,{},{a,b}], where f is some field name and a and b are two SU(N) indices. Again, with the option-setting Explicit True, an explicit expression is returned, depending on the setting on the other options. CovariantD[OPEDelta, a, b] is a short form for CovariantD[mu,a,b]*FourVector[OPEDelta, mu]. CovariantD[{OPEDelta, a, b}, {n}] yields the product of n operators, where n is an integer. CovariantD[OPEDelta, a, b, {m, n}] gives the expanded form of CovariantD[OPEDelta, a, b]^m up to order g^n for the gluon, where n is an integer and g the coupling constant indicated by the setting of the option CouplingConstant. CovariantD[OPEDelta, {m, n}] gives the expanded form of CovariantD[OPEDelta]^m up to order g^n of the fermionic field. Possible settings of PartialD are: LeftPartialD, LeftRigthPartialD, RightPartialD. The default setting of QuantumField is GaugeField.

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

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The first argument of CovariantD is intepreted as type LorentzIndex, except for OPEDelta, which is type Momentum.
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This givesthe partial derivative contracted with
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The expansion up to first order in the coupling constant
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The expansion up to second order in the
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