  In this paper, we study general mean-field backward stochastic differential
equations (BSDEs, for short) with quadratic growth. First, the existence and
uniqueness of local and global solutions are proved with some new ideas for a
one-dimensional mean-field BSDE when the generator $g\big(t, Y, Z,
\mathbb{P}_{Y}, \mathbb{P}_{Z}\big)$ has a quadratic growth in $Z$ and the
terminal value is bounded. Second, a comparison theorem for the general
mean-field BSDEs is obtained with the Girsanov transform. Third, we prove the
convergence of the particle systems to the mean-field BSDEs with quadratic
growth, and the convergence rate is also given. Finally, in this framework, we
use the mean-field BSDE to provide a probabilistic representation for the
viscosity solution of a nonlocal partial differential equation (PDE, for short)
as an extended nonlinear Feynman-Kac formula, which yields the existence and
uniqueness of the solution to the PDE.
