Relativistic mass corrections for rotating superconductors

The relativistic Hamiltonian and Dirac current density for a charged particle in a rotating frame are derived. Simple results are obtained correct to all orders in the particle velocity and to first order in the rotation velocity. An extension is made to the manyelectron current and is used for calculating the relativistic corrections to the magnetic field generated within a rotating superconductor (London moment). With the use of simple solid-state models, estimates of the corrections for common elemental superconductors are presented. The results predict several hundred ppm corrections for most superconductors and are of direct significance to high-precision measurements of $\frac{h}{m_e}$ now under way at Stanford. In addition, comparison of the experimental values with the accepted value of $\frac{h}{m_e}$ for the free electron at rest will provide a direct measure of the expectation value for the kinetic energy of the electron wave functions averaged over the Fermi surface, a quantity not observed directly by any other technique.