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.v1
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.v1
Kuntman, M.A. 4-Component Spinors for SL(4,C) and Four Types of Transformations. Preprints2023, 2023030540. https://doi.org/10.20944/preprints202303.0540.v1
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.v1
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.v1
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.
