Example 1.

First create a vector bundle M with base coordinates [x, y, z, t] and fiber coordinates [z1, z2, w1, w2].

Here are the 2 Kronecker delta spinors one can define:

Define some other manifold N.

The current frame is N.  Because there are no fiber variables, one cannot calculate a Kronecker delta spinor in this frame.  To now re-calculate the Kronecker delta spinor KK1, either use the ChangeFrame command or pass KroneckerDeltaSpinor the frame name M as a second argument.

Example 2.

The Kronecker delta spinor defines an identity mapping on spinors of the indicated type.  The linear transformation associated to the Kronecker delta spinor K is defined by contracting the covariant index of K against the contravariant index of the spinor S1.  We see that the result is S2 = S1 so that the linear transformation defined by K is indeed the identity transformation.

DifferentialGeometry, Tensor, BivectorSolderForm, CanonicalTensors, KroneckerDelta, PermutationSymbol, SolderForm