Commutators of the four-current and sum rules in relativistic nuclear models

There is a long-standing problem with the linearly energy-weighted sum of the excitation strengths in relativistic field theory and nuclear models: The sum value should be positive definite, while its naive calculation using the current commutator or the double commutator of the excitation operator with the Dirac Hamiltonian results in the value vanishing. This paradoxical contradiction is solved in an analytic way.