Quaternion Spin

Bryan Sanctuary ()
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Bryan Sanctuary: Department of Chemistry, McGill University, Montreal, QC H3A 0B8, Canada

Mathematics, 2024, vol. 12, issue 13, 1-15

Abstract: We present an analysis of the Dirac equation when the spin symmetry is changed from SU(2) to the quaternion group, Q 8 , achieved by multiplying one of the gamma matrices by the imaginary number, i . The reason for doing this is to introduce a bivector into the spin algebra, which complexifies the Dirac field. It then separates into two distinct and complementary spaces: one describing polarization and the other coherence. The former describes a 2D structured spin, and the latter its helicity, generated by a unit quaternion.

Keywords: dirac field; dirac equation; theoretical physicists; quantum field theory; quaternionic model; quantum theory (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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