On the question of the Wilson fermion doubling phenomenon on irregular lattice
S. N. Vergeles
Landau Institute for Theoretical Physics of the RAS, 142432 Chernogolovka, Russia
Department of Theoretical Physics, Moscow Institute of Physics and Technology, 141700 Dolgoprudnyj, Russia
It is shown that the Wilson fermion doubling
phenomenon on irregular lattices (simplicial complexes) does exist.
This means that the irregular (not smooth) zero or soft modes exist.
The statement is proved on 4-Dimensional lattice by means of the
Atiyah-Singer index theorem.