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BRST analysis of physical fields and states for 4D quantum gravity on<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi><mml:mo mathvariant="bold">×</mml:mo><mml:msup><mml:mi>S</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:math>
We consider the background-free quantum gravity based on conformal gravity with the Riegert-Wess-Zumino action, which is formulated in terms of a conformal field theory. Employing the $R \times S^3$ background in practice, we construct the nilpotent BRST operator imposing diffeomorphism invariance. Physical fields and states are analyzed, which are given …