Action principle for the connection dynamics of scalar-tensor theories
  A first-order action for scalar-tensor theories of gravity is proposed. The Hamiltonian analysis of the action gives the desired connection dynamical formalism, which was derived from the geometrical dynamics by canonical transformations. It is shown that this connection formalism in Jordan frame is equivalent to the alternative connection formalism in Einstein frame. Therefore, the action principle underlying loop quantum scalar-tensor theories is recovered. 
Zhenhua Zhou, Haibiao Guo, Yu Han and Yongge Ma
gr-qc