Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice

Details Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice

2004-01-13

arxiv.org/abs/hep-lat/0401019v1

J.Phys.A32:2481-2497,1999

Physics

High Energy Physics

High Energy Physics - Lattice

LaTeX, 20 pages, 1 eps figure, uses iopconf.sty (late submission)

Scientific paper

10.1088/0305-4470/32/12/019

We propose the fundamental and two dimensional representation of the Lorentz groups on a (3+1)-dimensional hypercubic lattice, from which representations of higher dimensions can be constructed. For the unitary representation of the discrete translation group we use the kernel of the Fourier transform. From the Dirac representation of the Lorentz group (including reflections) we derive in a natural way the wave equation on the lattice for spin 1/2 particles. Finally the induced representation of the discrete inhomogeneous Lorentz group is constructed by standard methods and its connection with the continuous case is discussed.

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