  We formulate a model for quantum gravity based on the local Lorentz symmetry
and general coordinate invariance. A key idea is the irreversible vierbein
postulate that a tree-level action for the model at a certain energy scale does
not contain an inverse vierbein. Under this postulate, only the spinor becomes
a dynamical field, and no gravitational background field is introduced in the
tree-level action. In this paper, after explaining the transformation rules of
the local Lorentz and general-coordinate transformations in detail, a
tree-level action is defined. We show that fermionic fluctuations can induce a
nonvanishing gravitational background field.
