2013/10/24 by Matej Pavšič, Pavšič, Matej
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · Physics and Astronomy · #Algebraic and Geometric Analysis #Biofield Effects and Biophysics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Microtubule and mitosis dynamics #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1310.6566
11 pages; Presented at 3rd International Conference on Theoretical Physics, Moscow, Russia, June 24 - 28, 2013
arxiv created 2013/10/24 · openalex publication_date 2013/10/24 · arxiv updated 2013/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that since the geometric spinors are elements of Clifford algebras, they must have the same transformation properties as any other Clifford number. In general, a Clifford number Φ transforms into a new Clifford number Φ' according to Φ→ Φ' = \rmR Φ \rmS, i.e., by the multiplication from the left and from the right by two Clifford numbers \rm R and \rm S. We study the case of Cl(1,3), which is the Clifford algebra of the Minkowski spacetime. Depending on choice of \rm R and \rm S, there are various possibilities, including the transformations of vectors into 3-vectors, and the transformations of the spinors of one minimal left ideal of Cl(1,3) into another minimal left ideal. This, among others, has implications for understanding the observed non-conservation of parity.