Abstract
By invoking the physical symmetry of coordinate invariance for the matter-free gravitational field, the contracted quantum Bianchi identities are derived from a family of Hermitian Lagrangians which are the quantum analogs of the Palatini Lagrangian. It is further shown that these gauge-variational techniques yield a set of necessary conditions that determine whether the quantum field equations and contracted Bianchi identities contain purely quantum structures of order ${\ensuremath{\hbar}}^{2}$ which possess no classical analogs.
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