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Vector spaces of (framed) BPS states of Lagrangian four-dimensional N=2 fieldtheories can be defined in semiclassical chambers in terms of the$L^2$-cohomology of Dirac-like operators on monopole moduli spaces. This wasspelled out previously for theories with only vectormultiplets, taking intoaccount only a subset of the possible half-supersymmetric 't Hooft-Wilson linedefects. This note completes the discussion by describing the modificationsneeded when including matter hypermultiplets together with arbitrary 'tHooft-Wilson line defects. Two applications of this extended discussion aregiven.

A Note On The Semiclassical Formulation Of BPS States In Four-Dimensional N=2 Theories