Example 1.

First create a vector bundle M with base coordinates [x, y, z, t] and fiber coordinates [z1, z2, w1, w2]. For spinor applications, it is tacitly assumed that [z1, z2] are complex coordinates with complex conjugates [w1, w2].

Define spinors S1 and S2 and calculate their complex conjugates.

Example 2.

The two type (1, 1) Kronecker delta spinors are complex conjugates of each other.

Example 3.

The soldering form is always a Hermitian spinor.  To check this calculate, first define the solder form sigma, then conjugate sigma and interchange the 2nd and 3rd indices.  The result is the original solder form sigma.

Example 4.

Use the Maple assuming command to simplify the complex conjugate of a spinor-tensor containing a real parameter alpha.

Example 6.

In some applications complex coordinates on the base space are used.  Suppose, for example, that z, t are real coordinates and that u is a complex coordinate with complex conjugate v.

Use the keyword argument conjugatecoordinates to specify that the conjugate of u is v (and the conjugate of v is u).

DifferentialGeometry, Tensor, assuming, DGmap, KroneckerDeltaSpinor, RearrangeIndices, SolderForm