Relativistic corrections are investigated to the Gamow–Teller (GT) sum rule with respect to the difference between the β- and β+ transition strengths in nuclei. Since the sum rule requires the complete set of the nuclear states, the relativistic corrections come from the anti-nucleon degrees of freedom. In the relativistic mean field approximation, the total GT strengths carried by the nucleon sector is quenched by about 12% in nuclear matter, while by about 8% in finite nuclei, compared to the sum rule value. The coupling between the particle-hole states with the nucleon–antinucleon states is also discussed with the relativistic random phase approximation, where the divergence of the response function is renormalized with use of the counterterms in the Lagrangian. It is shown that the approximation to neglect the divergence, like the no-sea approximation extensively used so far, is unphysical, from the sum-rule point of view.
Relativistic corrections to a generalized sum rule