论文标题
真正的Chern-Simons波函数
The real Chern-Simons wave function
论文作者
论文摘要
我们从仅使用真实连接和度量变量的重力表述的角度检查了Chern-Simons(或Kodama)状态的状态。我们可以将{\ it Real}连接变量包装到复杂的自动偶数Ashtekar连接中(并将与以前的工作联系起来),但是该操作本质上是化妆品,并且可以在任何步骤中撤消,甚至可以完全绕过。该动作将仍然是(真实的)爱因斯坦 - 卡丹(Einstein-Cartan)的作用,放弃了以假想系数的添加通常的Holst(或Nieh-Yan)术语。然后发现,约束是通过修改Chern-simons状态(在Lorentzian理论中,我们强调的)来解决的,该相位仅包含Chern-Simons功能的完全规范不变的想象部分。因此,“真实理论”的状态是关于其“非现实”堂兄面临的最严重的批评,解决了复杂理论。真实的Chern-Simons状态的直接修改也是基于Euler不变性的准理论理论的解决方案,宇宙学常数$λ$是动态的。在这种情况下,波动函数中的$λ$的通常因素是空间Chern-Simons积分的内部。技巧仅适用于准欧拉理论,其先前在文献中鉴定出来的关键耦合。它不适用于准综合素理论。
We examine the status of the Chern-Simons (or Kodama) state from the point of view of a formulation of gravity that uses only real connection and metric variables and a real action. We may package the {\it real} connection variables into the complex Self-Dual Ashtekar connection (and will do so to make contact with previous work), but that operation is essentially cosmetic and can be undone at any step or even bypassed altogether. The action will remain the (real) Einstein-Cartan action, forgoing the addition of the usual Holst (or Nieh-Yan) term with an imaginary coefficient. It is then found that the constraints are solved by a modification of the Chern-Simons state which is a pure phase (in the Lorentzian theory, we stress), the phase containing only the fully gauge-invariant imaginary part of the Chern-Simons functional. Thus, the state for the "real theory" is non-pathological with regards to the most egregious criticisms facing its "non-real" cousin, solving the complex theory. A straightforward modification of the real Chern-Simons state is also a solution in quasi-topological theories based on the Euler invariant, for which the cosmological constant, $Λ$, is dynamical. In that case it is enough to shift the usual factor of $Λ$ in the wave function to the inside of the spatial Chern-Simons integral. The trick only works for the quasi-Euler theory with a critical coupling previously identified in the literature. It does not apply to the quasi-Pontryagin theory.