Interference, gravity and gauge fields

Abstract

The phase shift due to gravitational field and all gauge fields in the interference of two coherent beams is obtained. In the case of gravitation, it is shown, for a particle with arbitrary spin, that there exists a phase shift due to the coupling of spin to space-time curvature. This and the corresponding phase shift for gauge fields are analogous to the Aharonov-Bohm effect. The classical limit for particles moving in gravitational and gauge fields is obtained from the phase shift. For gravitation, in the absence of torsion, this is the Mathisson-Papapetrou equation, which is thereby shown to be the classical limit of the Dirac and Bargmann-Wigner wave equations, generalized to curved space-time. In the presence of torsion, a modification of this equation, given by Hehl, is obtained. It is pointed out that gravity is not a pure gauge field and that it must be placed in the more general category of an «interference field» which contains both gravity and gauge fields as special cases. The field equations for gauge fields and gravity are obtained from the heuristic assumption that a particle acts on a field in a manner which depends on how it responds to the field via the phase shift. For gauge fields, they contain the Yang-Mills equations as a special case. For gravity, a modification of Einstein’s field equations is obtained, which corresponds to the Lagrangian (1/16πK) ·, · (2Λ +R) + (1/32πf)RμνϱσRμνσϱ, where the Riemann tensor contains torsion andK, f, Λ are constants (Λ may be zero). The relevance of the phase shift, due to rotation, to the quantization of vortices in superfluid helium is pointed out. This suggests that the curl of the superfluid velocity may obey a system of equations analogous to Maxwell’s equations and the analogue of the magnetic monopole for superfluid helium is also introduced.