Ginsparg-Wilson Relation and Ultralocality

It is shown that it is impossible to construct a free theory of fermions on infinite hypercubic Euclidean lattice in four dimensions that (a) is ultralocal, (b) respects symmetries of hypercubic lattice, (c) has a corresponding kernel that satisfies $\mathbf{D}{\ensuremath{\gamma}}_{5}+{\ensuremath{\gamma}}_{5}\mathbf{D}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\mathbf{D}{\ensuremath{\gamma}}_{5}\mathbf{D}$ (Ginsparg-Wilson relation), and (d) describes a single species of massless Dirac fermions in the continuum limit.