Abstract
A new class of multivector quantum mechanics is defined in which the theoretical gains over standard formalism are fully illustrated. Multiple generations of particles appear when column spinors are replaced by Clifford multivectors (matrices associated with physical geometry). New gauge fields arise from now-allowable right-side-applied transformations, independent of the usual left-sided ones. The number and group structure of the gauge generators is a function of the dimension and metric of the underlying geometric space, where constraints on a multivector Lagrangian suppress some interactions.
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References
J.S.R. Chisholm and R.S. Farwell,J. Phys. A22, 1059 (1989); “Unified spin gauge theories of the four fundamental forces” inThe Interface of Mathematics and Particle Physics, D.G. Quillen, G.B. Segal and S.T. Tsou, (Clarendon Press, Oxford1990), pp. 193-202.
D. Hestenes,Found. Phys. 12, 153 (1982);J. Math. Phys. 16, 556 (1975).
K. Greider,Found. Phys. 14, 467 (1984);Phys. Rev. Lett. 44, 1718 (1980).
I.M. Benn and R.W. Tucker,Commun. Math. Phys. 98, 53 (1985).
W. Pezzaglia, “Multivector solution to harmonic systems” inProceedings of the NATO and SERC Workshop on Clifford Algebras and Their Applications in Mathematical Physics, J.S.R. Chisholm and A.K. Common, eds. (NATO ASI Series C,183) (Reidel, Dordrecht 1986), pp. 445–454.
S.A. Basri and A.O. Barut,J. Math. Phys. 26, 1355 (1985).
E. Majorana,Nuovo Cimento 5, 171 (1937); N. Salingaros,Adv. Appl. Math. 4, 31 (1983).
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Pezzaglia, W.M. Clifford algebra geometric-multispinor particles and multivector-current gauge fields. Found Phys Lett 5, 57–62 (1992). https://doi.org/10.1007/BF00689796
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DOI: https://doi.org/10.1007/BF00689796