  Recently, a new path integral formulation of Loop Quantum Gravity (LQG) has
been derived in arXiv:1910.03763 from the reduced phase space formulation of
the canonical LQG. This paper focuses on the semiclassical analysis of this
path integral formulation. We show that dominant contributions of the path
integral come from solutions of semiclassical equations of motion (EOMs), which
reduces to Hamilton's equations of holonomies and fluxes ${h}(e),{p}^a(e)$ in
the reduced phase space $\mathcal{P}_\gamma$ of the cubic lattice $\gamma$:
$\dot{h}(e)=\{{h}(e),\, \mathbf{H}\}$, $\dot{p}^a(e)=\{{p}^a(e),\,
\mathbf{H}\}$, where $\mathbf{H}$ is the discrete physical Hamiltonian. The
semiclassical dynamics from the path integral becomes an initial value problem
of Hamiltonian time evolution in $\mathcal{P}_\gamma$. Moreover when we take
the continuum limit of the lattice $\gamma$, these Hamilton's equations
reproduce correctly classical reduced phase space EOMs of gravity coupled to
dust fields in the continuum, as far as initial and final states are
semiclassical. Our result proves that the new path integral formulation has the
correct semiclassical limit, and indicates that the reduced phase space
quantization in LQG is semiclassically consistent. Based on these results, we
compare this path integral formulation and the spin foam formulation, and show
that this formulation has several advantages including the finiteness, the
relation with canonical LQG, and being free of cosine and flatness problems.
