标题： 路径积分量子化$W_\infty$引力 显示英文标题

标题： Path-integral quantization of $W_\infty$ gravity

摘要： 我们从路径积分量子化的角度研究了$W_\infty$引力的反常性。 我们通过藤川方法直接从路径积分测度中推导出$\hbar$的幽灵圈反常到所有阶。 我们还表明，在物质领域，可以通过使用一阶反常来实现 Wess-Zumino 一致性条件以获得高阶环图反常。 这两个领域的反常相互抵消后，理论便无反常。 显示英文摘要

摘要： We consider the anomalies of $W_\infty$ gravity in the context of path-integralquantization. We derive the ghost-loop anomalies to all orders in $\hbar$ directly from the path-integral measure by the Fujikawa method. We also show that in the matter sector the higher-loop anomalies can be obtained by implementation of the Wess-Zumino consistency condition using the one-loop anomaly. Cancellation of the anomalies between these two sectors then leaves the theory anomaly-free.