Structure and different realizations of the extended real Clifford-Dirac algebra
V.M. Simulik, I.Yu. Krivsky, I.O. Gordievich, I.L. Lamer
TL;DR
This paper explores the structure and various realizations of the extended real Clifford-Dirac algebra, revealing its subalgebras and their applications in uncovering hidden symmetries of the Dirac equation.
Contribution
It introduces and analyzes the 64-dimensional ERCD algebra, its subalgebras, and demonstrates their use in deriving hidden symmetries of the Dirac equation.
Findings
Identified the 29-dimensional proper ERCD algebra.
Described the 32-dimensional invariance algebra of the Dirac equation.
Applied the algebra to derive hidden spin (1,0) Poincare symmetry.
Abstract
The structure of the 64-dimensional extended real Clifford-Dirac (ERCD) algebra, which has been introduced in our paper Phys. Lett. A. 375 (2011) 2479, is under consideration. The subalgebras of this algebra are investigated: the 29-dimensional proper ERCD algebra and 32-dimensional pure matrix algebra of invariance of the Dirac equation in the Foldy-Wouthuysen representation. The last one is the maximal pure matrix algebra of invariance of this equation. The different realizations of the proper ERCD algebra are given. The application of proper ERCD algebra is illustrated on the example of the derivation of the hidden spin (1,0) Poincare symmetry of the Dirac equation.
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Taxonomy
TopicsAlgebraic and Geometric Analysis · Noncommutative and Quantum Gravity Theories · Quantum Mechanics and Applications