The Rapid Communications section is intended for the accelerated publication of important new results. Since manuscripts submitted to this section are given priority treatment both in the editorial ofice and in production, authors should explain in their submittal letter why the work justifies this special handling. A Rapid Communication in Physical Review D should be no longer than five printed pages and must be accompanied by an abstract.A new method for calculating the covariant derivative expansions is presented, particularly in Abelian gauge theories, which can be used to find derivative expansions around nonvanishing gauge field-strength tensors. We apply this method to find the ad',,)*) terms of electron determinants in quantum electrodynamics.

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We consider the fourth-order conformal gravity theory. The quantization of the theory is presented in detail. We also calculate, using the heat kernel method, the one-loop divergence and conformal anomaly.

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