Quantum vortices of type II superconductors in curved space-time and Cattaneo's projection method

In this paper we show that the covariant dynamical equations of quantum vortices in type II superconductors may be brought into the same form as the classical equations written in 3-vector forms and can then be interpreted by using the familiar language of physics. This result is attained by introducing the physically measurable quantities by means of the corresponding standard relative quantities as defined by Cattaneo and by using his operator of transverse derivation, partial or covariant, with respect to the x4 lines. The standard equations thus obtained have a tensorial character and are covariant under the sole changes of coordinates leaving invariant the x4 lines, i.e. changes of coordinates internal to the physical system of reference S associated with the coordinates (xi). Expressions of the electric and magnetic fields induced inside a type II superconductor at rest in a curved space-time are obtained. The generation of these fields is influenced not only by the presence of a gravitational field but also by the presence of vortices. Comparison is made with the results predicted by the method of anholonomic frames.