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)
How to cite:
Kuntman, M. A. 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). Preprints2023, 2023030540. https://doi.org/10.20944/preprints202303.0540.v3
Kuntman, M. A. 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). Preprints 2023, 2023030540. https://doi.org/10.20944/preprints202303.0540.v3
Kuntman, M. A. 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). Preprints2023, 2023030540. https://doi.org/10.20944/preprints202303.0540.v3
APA Style
Kuntman, M. A. (2023). 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). Preprints. https://doi.org/10.20944/preprints202303.0540.v3
Chicago/Turabian Style
Kuntman, M. A. 2023 "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)" Preprints. https://doi.org/10.20944/preprints202303.0540.v3
Abstract
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).
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Commenter: Mehmet Ali Kuntman
Commenter's Conflict of Interests: Author