Tensor[NullVector] - construct a null vector from a solder form and a rank 1 spinor
Calling Sequences
NullVector(sigmaphi)
NullVector(sigmaphipsi)
Parameters
sigma - a spin-tensor defining a solder form on a 4-dimensional spacetime
phi, psi - rank 1 spinors
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Description
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With two arguments, the NullVector command returns the real vector with components
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• With three arguments, the NullVector command returns the (complex) vector with components
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This command is part of the DifferentialGeometry:-Tensor package, and so can be used in the form NullVector(...) only after executing the commands with(DifferentialGeometry); with(Tensor) in that order. It can always be used in the long form DifferentialGeometry:-Tensor:-NullVector.
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Examples
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Example 1.
First create the spinor bundle with spacetime coordinates and fiber coordinates .
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| (2.1) |
Define a spacetime metric on with signature .
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| (2.2) |
Define an orthonormal tetrad on with respect to the metric Use the command SolderForm to create a solder form .
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| (2.3) |
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| (2.4) |
Define rank 1 spinors and
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| (2.5) |
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| (2.6) |
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| (2.7) |
Use the command NullVector to find the corrresponding null vectors .
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| (2.8) |
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| (2.9) |
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| (2.10) |
We can use the command TensorInnerProduct to check that the vectors are indeed null vectors.
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| (2.11) |
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| (2.12) |
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| (2.13) |
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