The Lie algebra s o (N) and the Duffin-Kemmer-Petiau ring
- 1 January 1974
- journal article
- conference paper
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 15 (1) , 60-64
- https://doi.org/10.1063/1.1666504
Abstract
An explicit expression is given for the unit element E of the ring generated by the Duffin‐Kemmer‐Petiau (DKP) operators βμ. The relation of E to the unit operator I (unit matrix in a matrix representation) is also derived. It is pointed out that one must be careful to distinguish E from I. Bhabha's observation that one may use the irreducible representations (irreps) of the Lie algebra s o (5) to obtain the irreps of the Dirac, DKP, and other algebras is given a concise and general setting in terms of a relation between the Lie algebra s o (n + 1) and a family of semisimple operator rings. We emphasize that for the case n + 1 = 5 this means that there is an underlying relationship between the physical DKP and Dirac algebras and wave equations.Keywords
This publication has 18 references indexed in Scilit:
- Spin-0 Phenomenology ofDecays in the-Pole ModelPhysical Review D, 1973
- Resolution of the SU(3) Puzzle:Physical Review Letters, 1972
- Inequivalence of the Klein-Gordon and Kemmer Formulations ofDecayPhysical Review D, 1972
- Wave Equations with Compact and Noncompact SpectrumPhysical Review D, 1971
- Lowering and Raising Operators for the Orthogonal Group in the Chain O(n) ⊃ O(n − 1) ⊃ … , and their GraphsJournal of Mathematical Physics, 1967
- Dirac matrices and the Dirac matrix description of Lorentz transformationsCommunications in Mathematical Physics, 1966
- Representations of parafermi ringsNuclear Physics, 1963
- Relativistic Wave Equations for the Elementary ParticlesReviews of Modern Physics, 1945
- The algebra of meson matricesMathematical Proceedings of the Cambridge Philosophical Society, 1943
- Spinors in n DimensionsAmerican Journal of Mathematics, 1935