  As modified gravity theories, the 4-dimensional metric $f(R)$ theories are
cast into connection dynamical formalism with real $su(2)$-connections as
configuration variables. This formalism enables us to extend the
non-perturbative loop quantization scheme of general relativity to any metric
$f(R)$ theories. The quantum kinematical framework of $f(R)$ gravity is
rigorously constructed, where the quantum dynamics can be launched. Both
Hamiltonian constraint operator and master constraint operator for $f(R)$
theories are well defined. Our results show that the non-perturbative
quantization procedure of loop quantum gravity are valid not only for general
relativity but also for a rather general class of 4-dimensional metric theories
of gravity.
