Abstract
We analyse further the algebraic structure of dependent fermions, namely ones interrelated by the vertex operator construction. They are associated with special sorts of lattice systems which are introduced and discussed. The explicit evaluation of the relevant cocycles leads to the result that the operator product expansion of the fermions is related in a precise way to one or another of the division algebras given by complex numbers, quaternions or octonions. The latter case is seen to be realised in the light cone formalism of superstring theory.
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Communicated by A. Jaffe
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Goddard, P., Nahm, W., Olive, D.I. et al. Fermions and octonions. Commun.Math. Phys. 112, 385–408 (1987). https://doi.org/10.1007/BF01218483
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DOI: https://doi.org/10.1007/BF01218483