A comment on the magical realizations of W_3

Details A comment on the magical realizations of W_3 A comment on the magical realizations of W_3

1994-01-21

arxiv.org/abs/hep-th/9401108v1

Phys.Lett. B326 (1994) 89-94

Physics

High Energy Physics

High Energy Physics - Theory

.dvi file + 1 EPS figure, 10 document pages but 5 physical pages

Scientific paper

10.1016/0370-2693(94)91197-5

In the process of investigating classical realizations of W_3 in terms of free bosons, Romans unveiled a relation to finite-dimensional Jordan algebras with a cubic norm. These algebras have been classified and consist of an infinite series (yielding the ``generic'' realizations) and four sporadic algebras associated to the real division algebras (which yield the ``magical'' realizations). The generic realizations were shown by Romans to quantize, who left the problem of the quantization of the magical realizations open. In later work, Mohammedi showed that the first two magical realizations did not survive quantization. In this note we close the problem by showing that neither do the other two magical realizations.

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