Lattice Fermions Based on Higher-Dimensional Hyperdiamond Lattices

Abstract

In this paper we generalize to higher dimensions several types of fermion actions on the hyperdiamond lattice including a two-parameter class of minimal-doubling fermions "Creutz fermion" and a simple fermion with sufficient discrete symmetry "BBTW fermion". Then it is shown that they possess some properties in common with the four-dimensional case: BBTW fermions in higher even dimensions inevitably yield unphysical degrees of freedom. Creutz fermions are defined on the distorted lattices, and they lose the high discrete symmetry of the original lattices. We also find properties specific to the higher-dimensional cases. The parameter range for Creutz action to yield minimal-doubling and physical fermions becomes narrower with the dimension getting higher, thus it becomes more and more difficult to realize minimal-doubling. In addition, we generalize the subspecies of Creutz and BBTW actions including a new class of minimal-doubling actions "Appended Creutz action".

18 pages, 2 figures. To appear in Prog. Theo. Phys

References in corpus (7)

• The electronic properties of graphene
• Creutz Fermions on an Orthogonal Lattice
• Broken Symmetries from Minimally Doubled Fermions
• Minimally doubled fermions at one loop
• Search for Fermion Actions on Hyperdiamond Lattices
• Twisted Mass, Overlap and Creutz Fermions: Cut-off Effects at Tree-level of Perturbation Theory
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