FieldDerivative
FieldDerivative[f[x], x, li1, li2, ...]
is the derivative of f[x]
with respect to space-time variables x
and with Lorentz indices li1, li2, ...
, where li1, li2, ...
have head LorentzIndex
.
FieldDerivative[f[x], x, li1, li2, ...]
can be given as FieldDerivative[f[x], x, {l1, l2, ...}]
, where l1 is li1 without the head.
FieldDerivative
is defined only for objects with head QuantumField
. If the space-time derivative of other objects is wanted, the corresponding rule must be specified.
See also
Overview, FCPartialD, ExpandPartialD.
Examples
QuantumField[A, {\[Mu]}][x] . QuantumField[B, {\[Nu]}][y] . QuantumField[C, {\[Rho]}][x] . QuantumField[D, {\[Sigma]}][y]
Aμ(x).Bν(y).Cρ(x).Dσ(y)
FieldDerivative[%, x, {\[Mu]}] // DotExpand
Aμ(x).Bν(y).((∂μCρ))(x).Dσ(y)+((∂μAμ))(x).Bν(y).Cρ(x).Dσ(y)
FieldDerivative[%%, y, {\[Nu]}] // DotExpand
Aμ(x).Bν(y).Cρ(x).((∂νDσ))(y)+Aμ(x).((∂νBν))(y).Cρ(x).Dσ(y)