>
|
|
Example 1.
First create a vector bundle with base coordinates and fiber coordinates .
>
|
|
Define rank 1 spinors and and calculate their inner product.
M >
|
|
M >
|
|
M >
|
|
Note the sign change:
M >
|
|
The inner product of a rank 1 spinor with itself vanishes
M >
|
|
Calculate the inner product of and from the definition.
M >
|
|
| (2.7) |
M >
|
|
M >
|
|
Example 2.
Calculate the inner product of two rank 2 spinors and .
M >
|
|
| (2.10) |
M >
|
|
| (2.11) |
M >
|
|
Example 3.
Calculate the inner product of two rank 2 spinor-tensors and . Note that in this example the result is a rank 2 tensor.
M >
|
|
| (2.13) |
M >
|
|
| (2.14) |
M >
|
|