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Example 1.
First create a vector bundle with base coordinates and fiber coordinates .
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Here are the 4 epsilon spinors one can define:
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| (2.2) |
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| (2.3) |
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| (2.4) |
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| (2.5) |
Define some other manifold .
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The current frame is . Because there are no fiber variables, one cannot calculate an epsilon spinor in this frame. To now re-calculate the epsilon spinor , either use the ChangeFrame command or pass EpsilonSpinor the frame name as a third argument.
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Example 2.
The covariant and contravariant forms of the epsilon spinors are inverses of each other.
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| (2.9) |
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| (2.10) |
Contract the first index of with the first index of . The result is the Kronecker delta spinor.
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| (2.11) |
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