标题： 引力共形不变性与卡鲁扎-克莱因理论中的耦合常数 显示英文标题

标题： Gravitational conformal invariance and coupling constants in Kaluza-Klein theory

摘要： 我们在非紧致五维卡鲁扎-克莱因理论的背景下引入了一种广义的引力共形不变性。 这是通过假设四维度规依赖于额外的非紧致维度来实现的。 然后表明，通过在绝对宇宙学尺度$R_0$上取四维度规对第五维的依赖性较弱，五维中的共形不变性被破坏。 这相当于在理论中取一个常数宇宙质量项$\mu^2\sim R_0^{-2}$来导致四维中的共形不变性破坏。 我们将标量场设为其背景宇宙学值，从而得到具有引力常数$G_N$和一个小宇宙常数的爱因斯坦方程。 还引入了一个对偶的爱因斯坦方程，在其中物质通过耦合$G_N^{-1}$与高维几何耦合。 也讨论了结果的相关解释。 显示英文摘要

摘要： We introduce a generalized gravitational conformal invariance in the context of non-compactified 5D Kaluza-Klein theory. It is done by assuming the 4D metric to be dependent on the extra non-compactified dimension. It is then shown that the conformal invariance in 5D is broken by taking an absolute cosmological scale $R_0$ over which the 4D metric is assumed to be dependent weakly on the 5th dimension. This is equivalent to Deser's model for the breakdown of the conformal invariance in 4D by taking a constant cosmological mass term $\mu^2\sim R_0^{-2}$ in the theory. We set the scalar field to its background cosmological value leading to Einstein equation with the gravitational constant $G_N$ and a small cosmological constant. A dual Einstein equation is also introduced in which the matter is coupled to the higher dimensional geometry by the coupling $G_N^{-1}$. Relevant interpretations of the results are also discussed.