Sixteen Pairs of 4-Component Spinors for SL(4,C) and Four Types of Transformations with a Conjugate Space Which Has No Counterpart in SL(2,C)

Mehmet Ali Kuntman

doi:10.20944/preprints202303.0540.v3

Preprint Article Version 3 Preserved in Portico This version is not peer-reviewed

Version 1 : Received: 30 March 2023 / Approved: 31 March 2023 / Online: 31 March 2023 (03:35:26 CEST)
Version 2 : Received: 9 April 2023 / Approved: 11 April 2023 / Online: 11 April 2023 (03:27:31 CEST)
Version 3 : Received: 23 September 2023 / Approved: 25 September 2023 / Online: 25 September 2023 (09:34:12 CEST)

We define a spinor-Minkowski metric for SL(4,C). It is not a trivial generalization of the SL(2,C) metric and it involves the Minkowskian one. We define 4x4 version of the Pauli matrices and eight 4-component associated generalized eigenvectors that can be regarded as undotted covariant spinors. The 4-component spinors can be grouped into four categories. Each category transforms in its own way. The outer products of pairwise combinations of 4-component spinors can be associated with 4-vectors. Including the dotted covariant, undotted and dotted contravariant forms totally we have sixteen pairs of spinors. Eight of them live in the conjugate space which has no countepart in SL(2,C).

Lie Algebra; Lorentz group; SL(4,C); particle physics; polarization optics; nanoparticle interactions

Physical Sciences, Theoretical Physics

Comment 1

Received: 25 September 2023
Commenter: Mehmet Ali Kuntman
Commenter's Conflict of Interests: Author

Comment: New sections and figures are added.

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Sixteen Pairs of 4-Component Spinors for SL(4,C) and Four Types of Transformations with a Conjugate Space Which Has No Counterpart in SL(2,C)

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