Lattice calculations on the spectrum of Dirac and Dirac-Kähler operators

Details Lattice calculations on the spectrum of Dirac and Dirac-Kähler operators Lattice calculations on the spectrum of Dirac and Dirac-Kähler operators

2006-12-14

arxiv.org/abs/hep-lat/0612015v1

Int.J.Mod.Phys.A23:1029-1038,2008

Physics

High Energy Physics

High Energy Physics - Lattice

11 pages

Scientific paper

10.1142/S0217751X08038470

We present a matrix technique to obtain the spectrum and the analytical index of some elliptic operators defined on compact Riemannian manifolds. The method uses matrix representations of the derivative which yield exact values for the derivative of a trigonometric polynomial. These matrices can be used to find the exact spectrum of an elliptic operator in particular cases and in general, to give insight into the properties of the solution of the spectral problem. As examples, the analytical index and the eigenvalues of the Dirac operator on the torus and on the sphere are obtained and as an application of this technique, the spectrum of the Dirac-Kahler operator on the sphere is explored.

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