Absence of Neutrinos on a Lattice. 2: Intuitive Topological Proof

摘要

An intuitive topological proof is given of the no-go theorem for putting Weyl fermions in weak interaction on a lattice, or for constructing chiral invariant lattice QCD, which was proved by a homotypy theory argument previously. This theorem hangs on the existence of the charge (e.g., fermion number), and thus on the complex-field formulation and on locality. If the assumptions for the no-go theorem are relaxed, for instance the existence of the charge, and thus use the real-field formulation, a model can be constructed that has only one two-component field. This model can be assigned only an approximately conserved charge.