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

TL;DR

This paper resolves a long-standing paradox in relativistic nuclear models by analytically demonstrating that the sum of excitation strengths, which should be positive, is correctly obtained despite previous calculations suggesting it vanishes.

Contribution

The paper provides an analytic solution to the paradox of the sum rule in relativistic nuclear models, clarifying the correct calculation of excitation strength sums.

Findings

Analytic resolution of the sum rule paradox.

Confirmation that the sum value is positively definite.

Clarification of the proper calculation method for excitation strengths.

Abstract

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