Abstract
A spinor field equation, covariant with respect to the general conformal group (including reflections), should consist in general of not less than eight linear equations and then, in Minkowski space, could be represented by not less than two massless Dirac equations. Their reduction through projectors to only one equation, while not spoiling conformal covariance implies unphysical consequences. It is shown instead that two Dirac equations may be brought unambiguously through a stereographic projection to a manifestly conformal covariant form inE 4,2 space. The physical implications are discussed and it is shown that if the fundamental elementary interactions are expressed in terms of conformal semispinors (which can never appear as free particles), then the corresponding physical Dirac spinors appear in the elementary interactions in terms of their chiral projections. This could indicate both the conformally invariant origin of weak interactions and their fundamental character. The possibility of constructing unified models from conformally invariant Lagrangians is envisaged.
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Invited talk at the “Symposium on Mathematical Methods in the Theory of Elementary Particles”, Liblice castle, Czechoslovakia, June 18–23, 1978.
A preliminary version was issued as Internal Report IC/78/43, ICTP Trieste May 1978, see also Lett. Nuovo Cim.21 (1978), 473.
I am indebted to Prof. I. T.Todorov for interesting discussions.
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Budini, P. On conformally covariant spinor field equations. Czech J Phys 29, 6–21 (1979). https://doi.org/10.1007/BF01603799
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DOI: https://doi.org/10.1007/BF01603799