  Here, we clarify the physical aspects between the discrete Weyl-Wigner (W-W)
formalism, well developed in condensed matter physics, and the so-called
'precise Weyl-Wigner calculus for lattice models' recently appearing in the
literature. We point out that the use of compact continuous momentum space for
a discrete lattice model is unphysically founded. It has an incommensurate
phase space, highly unphysical, lacks the finite fields aspects, as exemplified
by the Born-von Karman boundary condition of compactified Bravais lattice of
solid-state physics, and leads to several ambiguities. This new W-W formalism
simply lacks bijective Fourier transformation, which is well-known to support
the uncertainty principle of canonical conjugate dynamical variables of quantum
physics. Moreover, this new W-W formalism for lattice models failed to handle
the quantum physics of qubits, representing two discrete lattice sites.
