2002/04/27 by P. P. Divakaran, Divakaran, P. P.
Physics and Astronomy · #Advanced Mathematical Theories and Applications #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #High Energy Physics - Theory (hep-th) #Noncommutative and Quantum Gravity Theories #Relativity and Gravitational Theory #hep-lat #hep-th
paper · pdf · doi:10.48550/arxiv.hep-lat/0204027
21 pages latex, 1 eps figure file
arxiv created 2002/04/27 · openalex publication_date 2002/04/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The lattice of integral points of 4-dimensional Minkowski space, together with the inherited indefinite distance function, is considered as a model for discrete space-time. The Lorentz and Poincare groups of this discrete space-time are identified as subgroups of the corresponding Lie groups. The lattice Lorentz group has irreducible projective (including linear) representations which are restrictions of (all) finite-dimensional irreducible projective representations of the Lorentz Lie group and hence can be used to describe all integral and half-odd-integral helicity. The (4-torus) momentum space has a well-defined ``light cone'' of null points and there are orbits of the lattice Lorentz group lying entirely in the torus light cone and having the lattice euclidean group of the plane as little group. Wigner's method for the Poincare Lie group can then be adapted to show, in the first instance, that the lattice Poincare group has unitary representations describing lattice free fields of zero mass and an arbitrary Lorentz helicity, in particular chiral fermions. There are no representations with a nonzero invariant mass.