Extension of loop quantum gravity to $f(R)$ theories

The 4-dimensional metric $f(\mathbb{R})$ theories of gravity are cast into connection-dynamical formalism with real $\text{SU}(2)$-connections as configuration variables. Through this formalism, the classical metric $f(\mathbb{R})$ theories are quantized by extending the loop quantization scheme of general relativity. Our results imply that the non-perturbative quantization procedure of loop quantum gravity is valid not only for general relativity but also for a rather general class of 4-dimensional metric theories of gravity.