Representation Mixing and Sum Rules for Magnetic Moments from Current Commutation Relations

Abstract

The commutation relation satisfied by the electric dipole moment operators is considered within the representation mixing scheme. By noting that the expectation value of the dipole moment operator for the nucleon at infinite momentum in the Z direction is the anomalous magnetic moment and its transformation property under the algebra U(3) × U(3) is {(8, 1)0 + (1, 8)0; LZ = ±1}, we show that from the commutation relation of the dipole moment operators a sum rule is derived which relates the anomalous magnetic moments of the proton and neutron with the isovector charge radius, where the assumption is made that the commutator is saturated by a few low-lying resonances. If we take into account the contribution of the second nucleon resonance N**(1512) to the commutator in addition to that of the nucleon and N*(1238), the sum rule predicts a reasonable value for the isovector rms charge radius.