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 $\mathbf{D}{\gamma }_5+{\gamma }_5\mathbf{D}=\mathbf{D}{\gamma }_5\mathbf{D}$ (Ginsparg-Wilson relation), and (d) describes a single species of massless Dirac fermions in the continuum limit.