Topological aspects of fermions on hyperdiamond
- Hassan II Academy of Science and Technology, Avenue Mohammed VI, KM 4, Souissi, Rabat (Morocco)
Motivated by recent results on the index of the Dirac operator D={gamma}{sup {mu}}D{sub {mu}} of QCD on lattice and also by results on topological features of electrons and holes of two-dimensional graphene, we compute in this paper the index of D for fermions living on a family of even-dimensional lattices denoted as L{sub 2N} and describing the 2N-dimensional generalization of the graphene honeycomb. The calculation of this topological index is done by using the direct method based on solving explicitly the gauged Dirac equation and also by using specific properties of the lattices L{sub 2N}, which are shown to be intimately linked with the weight lattices of SU(2N+ 1). The index associated with the two leading N= 1 and N= 2 elements of this family describe precisely the chiral anomalies of graphene and QCD{sub 4}. Comments on the method using the spectral flow approach as well as the computation of the topological charges on 2-cycles of 2N-dimensional compact supercell in L{sub 2N} and applications to QCD{sub 4} are also given.
- OSTI ID:
- 22093645
- Journal Information:
- Journal of Mathematical Physics, Vol. 53, Issue 7; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0022-2488
- Country of Publication:
- United States
- Language:
- English
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