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Example 1.
First create a vector bundle with base coordinates and fiber coordinates .
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Define a contravariant rank 1 spinor and lower its indices, that is, convert it to a covariant rank 1 spinor .
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| (2.2) |
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Define the covariant epsilon spinor and check that this result coincides with the contraction of and .
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| (2.4) |
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Convert back to a contravariant rank 1 spinor, recovering .
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Example 2.
Define a rank 4 spinor-tensor and raise its 2nd index and lower its 4th index.
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| (2.7) |
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| (2.8) |