AI 中文总结
本文将共形物质场相关结果推广至多耦合共形量子引力，利用BRST对称性证明其单圈共形不变重整化，并给出半经典理论中单圈发散的详细一般性证明。
AI 中文摘要
若所考虑的理论具有规范不变性，弯曲时空中经典共形理论的单圈发散是一个非平凡问题。在此情况下，量子化需引入规范固定项与鬼场作用量，二者均不具备共形性。1984年，本文作者之一已给出该情形下（含相互作用理论）共形不变重整化的形式证明。由于BRST对称性，规范固定与鬼场部分对有效作用量共形变分的贡献相互抵消，但该抵消在单圈及更高圈有效作用量的有限部分不成立，从而导致反常。本文将早期关于外引力场中共形物质场的结果推广并应用于共形量子引力，包括共形引力与其他共形物质场耦合的情形。尽管Weyl平方引力中的规范固定更为复杂，但利用BRST对称性证明单圈共形不变重整化是可行的。作为共形量子引力的预备工作，本文还给出了相应半经典理论中共形不变单圈发散的详细一般性证明。
英文摘要
One-loop divergences in classically conformal theory in curved spacetime is a nontrivial issue if the theory under consideration possesses gauge invariance. In this case, quantization involves introducing the gauge-fixing term and the action of ghosts, both of which are not conformal. The formal proof of the conformal invariant renormalizability in this situation, including interacting theories, has been given in the paper from 1984 by one of the present authors. Owing to BRST symmetry, the contributions of the gauge-fixing and ghost sectors to the conformal variation of the effective action cancel each other. This cancellation does not hold in the finite part of the one-loop and higher-loops effective action, that results in the anomaly. In this paper, we extend the early results on conformal matter fields in external gravitational field and apply them to conformal quantum gravity, including the case of conformal gravity coupled to other conformal matter fields. The gauge-fixing in the Weyl-squared gravity is more complicated, nevertheless, the proof of the one-loop conformal invariant renormalization using BRST symmetry is possible. As a preliminary to conformal quantum gravity, we also present a detailed general proof of conformal invariant one-loop divergences in the corresponding semiclassical theory.
Comments29 pages, LaTeX, no figures
