# Generalized Madelung transformations for quantum wave equations I: generalized spherical coordinates for field spaces - High Energy Physics - Theory

Generalized Madelung transformations for quantum wave equations I: generalized spherical coordinates for field spaces - High Energy Physics - Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: The Madelung transformation of the space in which a quantum wave functiontakes its values is generalized from complex numbers to include field spacesthat contain orbits of groups that are diffeomorphic to spheres. The generalform for the resulting real wave equations then involves structure constantsfor the matrix algebra that is associated with the group action. The particularcases 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.

Author: ** David Delphenich**

Source: https://arxiv.org/