  In this report, we discuss some theoretical and practical progresses in the
HAL QCD potential method. We first clarify the issue of the derivative
expansion for the non-local potential in the HAL QCD method. As the non-local
potential in the original literature is not uniquely defined, we propose a
procedure to define a non-local potential from NBS wave functions in terms of
the derivative expansion. We then demonstrate how this definition works by
using quantum mechanics with a separable potential. Secondly we discuss an
issue of Hermiticity of the HAL QCD potential. Since the NBS wav functions are
not orthogonal to each other in general, the HAL QCD potential is necessary to
be non-Hermitian. We consider the next-to-leading order potential, which can be
made Hermitian exactly by the change of variables. In general we can also make
the higher order HAL QCD potential Hermitian order by order in the derivative
expansion. An explicit example on how the procedure works is given for lattice
QCD calculations. Finally we discuss how we can extract the HAL QCD potential
from the NBS wave function in the boosted system. An explicit formula for this
is derived.
