Laplacians in polar matrix coordinates and radial fermionization in higher dimensions

Details Laplacians in polar matrix coordinates and radial fermionization in higher dimensions Laplacians in polar matrix coordinates and radial fermionization in higher dimensions

2009-11-15

arxiv.org/abs/0911.2846v1

J.Math.Phys.52:032302,2011

Physics

High Energy Physics

High Energy Physics - Theory

Latex, 15 pages

Scientific paper

10.1063/1.3553456

We consider the quantum mechanical hamiltonian of two, space indexed, hermitean matrices. By introducing matrix valued polar coordinates, we obtain the form of the laplacian acting on invariant states. For potentials depending only on the eigenvalues of the radial matrix, we establish that the radially invariant sector is equivalent to a system of non interacting 2+1 dimensional fermions, and obtain its density description. For a larger number of matrices, the presence of a repulsive radial inter-eigenvalue potential is identified.

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