Dirac-bracket structure in multidimensional mode conversion

► A geometrical representation of the tangent plane to the conversion manifold for multidimensional mode conversion. ► The definition of a Dirac-bracket structure on the tangent plane to the conversion manifold. ► The decomposition of the volume form in ray phase space in terms of the orthogonal and Dirac forms. ► The description of mode conversion in terms of transmission and conversion coefficients relating asymptotic ray actions.