R. Hammer, W. Pötz, A. Arnold:

"Single-cone real-space nite di erence scheme for the time-dependent Dirac equation";

in: "ASC Report 27/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 21.

A nite di erence scheme for the numerical treatment of the (3+1)D Dirac equation is presented. Its staggered-grid intertwined discretization treats space and time coordinates on equal footing, thereby avoiding the notorious fermion doubling problem. This explicit scheme operates entirely in real space and leads to

optimal linear scaling behavior for the computational e ort per space-time grid-point. It allows for an easy and e cient parallelization. A functional for a norm on the grid is identi ed. It can be interpreted as probability density and is proved to be conserved by the scheme. The single-cone dispersion relation

is shown and exact stability conditions are derived. Finally, a single-cone scheme and its properties are presented for the two-component (2+1)D Dirac equation.

Dirac equation, leap-frog, staggered grid, fermion doubling, FDTD

http://www.asc.tuwien.ac.at/preprint/2013/asc27x2013.pdf

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