LORENTZ TRANSFORMATIONS AND DIRAC SPINOR
By
J. D. Bulnes1, M. A. I. Travassos2 , J. LÓpez-Bonilla3 , S. Vidal-Beltrán4 , R. Rajendra5* and P. Siva Kota Reddy6
1,2Departamento de Ciˆencias Exatas e Tecnologia Universidade Federal do Amap´a Rod. J. Kubitschek, Macapá, AP, Brazil - 68903-419
3,4ESIME-Zacatenco, Instituto Politècnico Nacional Edif. 4, 1er. Piso, Col. Lindavista CP CDMX, Mexico-07738
5Department of Mathematics, Field Marshal K. M. Cariappa College, Madikeri, India - 571 202
6Department of Mathematics, JSS Science and Technology University, Mysuru, India - 570 006
Email: bulnes@unifap.br, angelicaptravass@gmail.com, jlopezb@ipn.mx, svidalb@ipn.mx, rrajendrar@gmail.com, pskreddy@jssstuniv.in
*Corresponding author
(Received: June 22, 2025; In format: September 23, 2025; Revised: October 28, 2025; Accepted: October 31, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55218
Abstract
This work constructs Lorentz transformations and Dirac spinor mappings using two complex 2 × 2 matrices under a unimodular condition. The approach leverages Pauli matrices and Hermitian conjugates to derive the spinor transformation matrix. It demonstrates equivalence with Macfarlanes formula and Veblens construction. The framework clarifies the role of InfeldVan der Waerden symbols in linking spacetime and spinor structures. This compact method highlights the symmetry principles underlying relativistic quantum theory.
2020 Mathematical Sciences Classification: 15A66, 83A05, 83C60.
Keywords and Phrases: Gamma matrices, Lorentz matrix, Dirac 4-spinor, Infeld-van der Waerden symbols, Unimodular matrix, Pauli matrices.