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

Irreversible vierbein postulate: Emergence of spacetime from quantum phase transition