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The Full Laplace-Beltrami operator on U(N) and SU(N)

The Laplacian on the Lie groups U(N) and SU(N) is given in a parametrized edition for practical purposes. The radial part is often seen in work on lattice gauge theory, but here is derived also the off-diagonal part which in SU(3) and U(3) is expressed via the well known Gell-Mann matrices but with a more easily memorized notation. Relations to I, U and V spin are also shown.

preprint2012arXivOpen access
O. L. TrinhammerG. Olafsson
math-phmath.MP
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O. L. TrinhammerG. Olafsson

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