1,366 research outputs found
Four Dimensional Graphene
Mimicking pristine 2D graphene, we revisit the BBTW model for 4D lattice QCD
given in ref.[5] by using the hidden SU(5) symmetry of the 4D hyperdiamond
lattice H_4. We first study the link between the H_4 and SU(5); then we refine
the BBTW 4D lattice action by using the weight vectors \lambda_1, \lambda_2,
\lambda_3, \lambda_4, \lambda_5 of the 5-dimensional representation of SU(5)
satisfying {\Sigma}_i\lambda_i=0. After that we study explicitly the solutions
of the zeros of the Dirac operator D in terms of the SU(5) simple roots
\alpha_1, \alpha_2, \alpha_3, \alpha_4 generating H_4; and its fundamental
weights \omega_1, \omega_2, \omega_3, \omega_4 which generate the reciprocal
lattice H_4^\ast. It is shown, amongst others, that these zeros live at the
sites of H_4^\ast; and the continuous limit D is given by ((id\surd5)/2)
\gamma^\muk_\mu with d, \gamma^\mu and k_\mu standing respectively for the
lattice parameter of H_4, the usual 4 Dirac matrices and the 4D wave vector.
Other features such as differences with BBTW model as well as the link between
the Dirac operator following from our construction and the one suggested by
Creutz using quaternions, are also given.
Keywords: Graphene, Lattice QCD, 4D hyperdiamond, BBTW model, SU(5) Symmetry.Comment: LaTex, 26 pages, 1 figure, To appear in Phys Rev
German Science Center for the Solar Dynamics Observatory
A data and computation center for helioseismology has been set up at the Max
Planck Institute for Solar System Research in Germany to prepare for the SDO
mission. Here we present the system infrastructure and the scientific aims of
this project, which is funded through grants from the German Aerospace Center
and the European Research Council
On Dirac Zero Modes in Hyperdiamond Model
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 {\Omega}_{{\mu}}^{l} with 4\times5 complex components linking the
Euclidean SO(4) vector {\mu}; and the 5-dimensional representation of SU(5).
The Bori\c{c}i-Creutz (BC) and the Karsten-Wilzeck (KW) models as well as their
Dirac zero modes are rederived as particular realizations of
{\Omega}_{{\mu}}^{l}. Other features are also given. Keywords: Lattice QCD,
Bori\c{c}i-Creutz and Karsten-Wilzeck models, 4D hyperdiamond, 4D graphene,
SU(5) Symmetry.Comment: LaTex, 28 pages, To appear in Phys Rev
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