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. 4-Component Spinors for SL(4,C) and Four Types of Transformations. Preprints2023, 2023030540. https://doi.org/10.20944/preprints202303.0540.v2
Kuntman, M. A. 4-Component Spinors for SL(4,C) and Four Types of Transformations. Preprints 2023, 2023030540. https://doi.org/10.20944/preprints202303.0540.v2
Kuntman, M. A. 4-Component Spinors for SL(4,C) and Four Types of Transformations. Preprints2023, 2023030540. https://doi.org/10.20944/preprints202303.0540.v2
APA Style
Kuntman, M. A. (2023). 4-Component Spinors for SL(4,C) and Four Types of Transformations. Preprints. https://doi.org/10.20944/preprints202303.0540.v2
Chicago/Turabian Style
Kuntman, M. A. 2023 "4-Component Spinors for SL(4,C) and Four Types of Transformations" Preprints. https://doi.org/10.20944/preprints202303.0540.v2
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 Minkowski metric. We define 4x4 version of the Pauli matrices and their 4-component generalized eigenvectors. The generalized eigenvectors can be regarded as 4-component spinors and they 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.
Keywords
Lie Algebra; Particle Physics; quantum mechanics
Subject
Physical Sciences, Theoretical Physics
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