Abstract
We raise the question if the fermion number (F = B + L) is absolutely conserved. Neutrinoless double-β-decay experiments give upper limits on ¦ΔL¦ = 2 transitions. Experiments on the stability of the deuteron against decay into pions would give analogous limits on ¦ΔB¦ = 6 transitions, while proton stability experiments set limits on ¦δF¦ = 0, ΔB = - ΔL as well as on transitions involving ¦ΔF¦≠ 0. HereB = + 1 for (integer or zero charge) quarks,B = -1 for antiquarks, whileL is the lepton number. Remarking that the maximal symmetry group for the kinematic-energy terms of a set ofn four-component Dirac fields isSU2n rather than U1 xSULn XSURn (with the extra gauge currents carrying fermion number ±2), we briefly investigate the possibility of constructing spontaneously broken gauge theories where the fermion number appears as a non-Abelian generator.
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