CovariantD

Description

CovariantD[mu, a, b] is the covariant derivative for a bosonic field. CovariantD[mu] is the covariant derivative for a fermionic field. 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 m 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 couplingconstant 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.

Options[CovariantD]

Possible settings of PartialD are: LeftPartialD, LeftRigthPartialD, RightPartialD. The default setting of QuantumField is GaugeField.

See also:  LeftPartialD, LeftRightPartialD, RightPartialD.

Examples

CovariantD[μ]

CovariantD[μ, a, b]

CovariantD[μ, Explicit -> True]

The first argument of CovariantD is intepreted as type LorentzIndex, except for OPEDelta, which is type Momentum.

CovariantD[OPEDelta]

CovariantD[OPEDelta, a, b]

CovariantD[OPEDelta, a, b, Explicit -> True]

CovariantD[OPEDelta, Explicit -> True]

CovariantD[OPEDelta, a, b, {2}]

This gives\(TraditionalForm\`\(\(\ \)\(m\ times\ \(∂\& → \)\_Δ\)\(,\)\(\ \)\)\)the partial derivative \(TraditionalForm\`\(∂\& → \)\_\(\(μ\)\(\ \)\)\)contracted with (Δ^μ).

CovariantD[OPEDelta, a, b, {OPEm, 0}]

The expansion up to first order in the coupling constant (Subscript[g, s]) (the  sum  is  the  FeynCalc  
              OPESum).

CovariantD[OPEDelta, a, b, {OPEm, 1}]

The expansion up to second order in the (Subscript[g, s]).

CovariantD[OPEDelta, a, b, {OPEm, 2}]

CovariantD[OPEDelta, a, b]^OPEm

CovariantD[OPEDelta, {OPEm, 2}]

CovariantD[OPEDelta, Explicit -> True] // StandardForm

CovariantD[μ, a, b, Explicit -> True] // StandardForm