关于纯引力共形反常

本文采用几何和拓扑的方法,讨论弯曲时空中的纯引力共形反常,并得到了纯引力共形反常的新的表达式αε^abcdΩ_abΛΩ_cd+βε^abcd H_abΛH_cd,其中α,β是任意常数,Ω_ab与H_ab分别是Riemann曲率2-形式与Thomas引入的共形不变曲率2-形式。这里,第一项正比于Euler类,第二项除了包含通常熟知的Wegl张量平方项以外,还含有其它共形不变的不变量。 关键词：

ON THE CONFORMAL ANOMALY FOR PURE GRAVITY

Based upon the geometrical and topological method, the conformal anomaly for pure gravity in a curved space-time is discussed, and a new expression αε^abcdΩ_abΛΩ_cd+βε^abcdH_abΛH_cd of the conformal anomaly for pure gravity is obtained, where α, βare two arbitrary constants,Ω_ab and H_ab are Riemann curvature 2-form and eonformal invariant curvature 2-form respectively introduced by Thomas. In the expression the first term is proportional to Euler class, the second term contains not only the ordinary Weyl tensor square but also the other conformal invariants.