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Spinors and the Weyl tensor classification in six dimensions
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10.1063/1.4804991
/content/aip/journal/jmp/54/5/10.1063/1.4804991
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/5/10.1063/1.4804991
View: Tables

Tables

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Table I.

Spinorial equivalent of tensors. is a vector, is a trace-less symmetric tensor, is a 2-vector,  is a 3-vector, and is a tensor with the symmetries of a Weyl tensor.

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Table II.

Some algebraically special types for the Weyl tensor. The labels come from: Repeated(R), Simple(S), and Non-Simple(NS). Here , and . The types , , and can obviously be defined, as well as many other special types.

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Table III.

Definition of the CMPP types. The second row says which components of the Weyl tensor should vanish according to the boost weight, . For example, when the type is all components of boost weight two must vanish in some null frame.

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Table IV.

The boost weight of the various components of

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Table V.

The spinorial representation of a bivector basis. The last four lines the inverse relation of the 3 short lines at the center.

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Table VI.

This table displays the relation between Weyl tensor's components in a null frame and its spinorial equivalent. The missing components of the Weyl tensor can be obtained by making the changes 1 ↔ 4, 2 ↔ 5, and 3 ↔ 6 on the vectorial indices while swapping the upper and the lower indices of Ψ. The first two rows contain the components of the Weyl tensor with boost weight = 2, the next ten rows present the components with = 1, the other rows have the components with zero boost weight.

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/content/aip/journal/jmp/54/5/10.1063/1.4804991
2013-05-21
2014-04-16
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Spinors and the Weyl tensor classification in six dimensions
http://aip.metastore.ingenta.com/content/aip/journal/jmp/54/5/10.1063/1.4804991
10.1063/1.4804991
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