The Kronecker delta spinor is the type $\left(\genfrac{}{}{0ex}{}{1}{1}\right)$ spinor whose components in any coordinate system are given by the identity matrix.

The command KroneckerDeltaSpinor(spinorType) returns a Kronecker delta spinor of the type specified by spinorType in the current frame unless the frame is explicitly specified.

This command is part of the DifferentialGeometry:-Tensor package, and so can be used in the form KroneckerDeltaSpinor(...) only after executing the commands with(DifferentialGeometry); with(Tensor); in that order. It can always be used in the long form DifferentialGeometry:-Tensor:-KroneckerDeltaSpinor.

$\mathrm{with}\left(\mathrm{DifferentialGeometry}\right)\:$$\mathrm{with}\left(\mathrm{Tensor}\right)\:$

$\mathrm{DGsetup}\left(\left[x\,y\,z\,t\right]\,\left[\mathrm{z1}\,\mathrm{z2}\,\mathrm{w1}\,\mathrm{w2}\right]\,M\right)$

$\mathrm{frame\; name:\; M}$

$\mathrm{K1}≔\mathrm{KroneckerDeltaSpinor}\left(''spinor''\right)$

$\mathrm{K1}:=\mathrm{D\_z1}\mathrm{dz1}+\mathrm{D\_z2}\mathrm{dz2}$

$\mathrm{K2}≔\mathrm{KroneckerDeltaSpinor}\left(''barspinor''\right)$

$\mathrm{K2}:=\mathrm{D\_w1}\mathrm{dw1}+\mathrm{D\_w2}\mathrm{dw2}$

$\mathrm{DGsetup}\left(\left[x\,y\,z\,t\right]\,N\right)$

$\mathrm{frame\; name:\; N}$

$\mathrm{KroneckerDeltaSpinor}\left(''spinor''\,M\right)$

$\mathrm{D\_z1}\mathrm{dz1}+\mathrm{D\_z2}\mathrm{dz2}$

$\mathrm{DGsetup}\left(\left[x\,y\,z\,t\right]\,\left[\mathrm{z1}\,\mathrm{z2}\,\mathrm{w1}\,\mathrm{w2}\right]\,M\right)$

$\mathrm{frame\; name:\; M}$

$K≔\mathrm{KroneckerDeltaSpinor}\left(''spinor''\right)$

$K:=\mathrm{D\_z1}\mathrm{dz1}+\mathrm{D\_z2}\mathrm{dz2}$

$\mathrm{S1}≔\mathrm{evalDG}\left(a\mathrm{D\_z1}+b\mathrm{D\_z2}\right)$

$\mathrm{S1}:=a\mathrm{D\_z1}+b\mathrm{D\_z2}$

$\mathrm{S2}≔\mathrm{ContractIndices}\left(\mathrm{S1}\,K\,\left[\left[1\,2\right]\right]\right)$

$\mathrm{S2}:=a\mathrm{D\_z1}+b\mathrm{D\_z2}$