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A microscopic analysis of the non-dissipative force F_nd acting on a linevortex in a type-II superconductor at T=0 is given. All work assumes a chargedBCS superconductor. We first examine the Berry phase induced in the BCS groundstate by movement of the vortex and show how this phase enters into thehydrodynamic action S_hyd of the condensate. Appropriate variation of S_hydgives F_nd and variation of the Berry phase term is seen to contribute theMagnus force of classical hydrodynamics to F_nd. This analysis confirms indetail the arguments of Ao and Thouless within the context of the BCS model.Our Berry phase, in the limit e -> 0, reproduces the Berry phase they obtainfor a neutral superfluid. A second independent determination of F_nd is giventhrough a microscopic derivation of the continuity equation for the condensatelinear momentum. This yields the acceleration equation for the superflow. Thevortex is seen to act as a momentum sink and the rate of momentum loss yieldsF_nd. Both calculations yield the same F_nd and show that the Magnus forcecontribution to F_nd is a consequence of the vortex motion and topology.Comment: abbrev. version of cond-mat/9408025, 4 pages, RevTex, no figure

Microscopical analysis of the non-dissipative force on a line vortex in a superconductor