Fermions with no fundamental charges call for extra dimensions
Abstract
We call attention to that if assuming no conserved charges in the fundamental theory with fermions, which carry only a spin and interact with only the gravity, the dimensions 4, 12, 20,....., as well as all odd dimensions, are excluded under the requirement of mass protection. If more than one family is required, than only dimensions d=2 (mod 4) remains as acceptable, since then other by 4 devisable dimensions are excluded.
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