Generalized Madelung transformations for quantum wave equations I: generalized spherical coordinates for field spaces

Details Generalized Madelung transformations for quantum wave equations I: generalized spherical coordinates for field spaces Generalized Madelung transformations for quantum wave equations I: generalized spherical coordinates for field spaces

2008-02-03

arxiv.org/abs/0802.0305v1

Physics

High Energy Physics

High Energy Physics - Theory

42 pages

Scientific paper

The Madelung transformation of the space in which a quantum wave function takes its values is generalized from complex numbers to include field spaces that contain orbits of groups that are diffeomorphic to spheres. The general form for the resulting real wave equations then involves structure constants for the matrix algebra that is associated with the group action. The particular cases of the algebras of complex numbers, quaternions, and complex quaternions, which pertain to the Klein-Gordon equation, the relativistic Pauli equation, and the bi-Dirac equation, resp., are then discussed.

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