Laplacians in polar matrix coordinates and radial fermionization in higher dimensions
Journal Article
·
· Journal of Mathematical Physics
- National Institute for Theoretical Physics, School of Physics and Centre for Theoretical Physics, University of the Witwatersrand, Johannesburg, Wits 2050 (South Africa)
We consider the quantum mechanical Hamiltonian of two, space indexed, Hermitian 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 noninteracting 2 + 1 dimensional fermions and obtain its density description. For a larger number of matrices, the presence of a repulsive radial intereigenvalue potential is identified.
- OSTI ID:
- 21501287
- Journal Information:
- Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 3 Vol. 52; ISSN JMAPAQ; ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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