Demanding associativity of the momentum translation operator for Schwinger's non-commuting coordinates of massless particles yields the helicity quantization λ=(ℏ/2)n, shown to be dual to Dirac's monopole quantization.
Small magnetic charges and monopoles in non-associative quantum mechanics
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abstract
Weak magnetic monopoles with a continuum of charges less than the minimum implied by Dirac's quantization condition may be possible in non-associative quantum mechanics. If a weakly magnetically charged proton in a hydrogen atom perturbs the standard energy spectrum only slightly, magnetic charges could have escaped detection. Testing this hypothesis requires entirely new methods to compute energy spectra in non-associative quantum mechanics. Such methods are presented here, and evaluated for upper bounds on the magnetic charge of elementary particles.
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Schwinger's non-commutative coordinates and duality between helicity and Dirac quantisation conditions
Demanding associativity of the momentum translation operator for Schwinger's non-commuting coordinates of massless particles yields the helicity quantization λ=(ℏ/2)n, shown to be dual to Dirac's monopole quantization.