Abstract
Using the SU(5) symmetry of the 4D hyperdiamond and results on the study of 4D graphene given in "Four Dimensional Graphene" (L.B Drissi, E.H Saidi, M. Bousmina, CPM-11-01, Phys. Rev. D (2011)), we engineer a class of 4D lattice QCD fermions whose Dirac operators have two zero modes. We show that generally the zero modes of the Dirac operator in hyperdiamond fermions are captured by a tensor Ω_{μ}^{l} with 4\times5 complex components linking the Euclidean SO(4) vector μ; and the 5-dimensional representation of SU(5). The Boriçi-Creutz (BC) and the Karsten-Wilzeck (KW) models as well as their Dirac zero modes are rederived as particular realizations of Ω_{μ}^{l}. Other features are also given. Keywords: Lattice QCD, Boriçi-Creutz and Karsten-Wilzeck models, 4D hyperdiamond, 4D graphene, SU(5) Symmetry.
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