论文标题
广泛的hartle-hawking波函数
A generalized Hartle-Hawking wavefunction
论文作者
论文摘要
众所周知，使用覆盖整个真实线的集成轮廓，hartle-hawking Wave函数是将Chern-Simons或Kodama状态减少到迷你Superspace的傅立叶双重函数。但是，由于Chern-Simons状态是汉密尔顿约束（带有给定的订单）的一般解决方案，因此其傅立叶双重二元应提供代表指标表示汉密尔顿约束的Wheeler Dewitt方程的一般解决方案（即超出迷你 - 苏普斯空间）。我们写下了这样的波函数的形式表达式，被视为超出hartle-hawking波函数的迷你超级空间的概括。它的明确评估（或简化）仅取决于问题的对称性，我们用各向异性比安奇模型和Kantowski-Sachs模型说明了程序。这种方法的一个显着差异是，当我们为连接设置ANSATZ时，我们可能会将扭转在波功能内部放置，而不是在量化之前将其设置为零。这允许扭转中的量子波动，并产生遥远的后果。
The Hartle-Hawking wave function is known to be the Fourier dual of the Chern-Simons or Kodama state reduced to mini-superspace, using an integration contour covering the whole real line. But since the Chern-Simons state is a general solution of the Hamiltonian constraint (with a given ordering), its Fourier dual should provide the general solution (i.e. beyond mini-superspace) of the Wheeler DeWitt equation representing the Hamiltonian constraint in the metric representation. We write down a formal expression for such a wave function, to be seen as the generalization beyond mini-superspace of the Hartle-Hawking wave function. Its explicit evaluation (or simplification) depends only on the symmetries of the problem, and we illustrate the procedure with anisotropic Bianchi models and with the Kantowski-Sachs model. A significant difference of this approach is that we may leave the torsion inside the wave functions when we set up the ansatz for the connection, rather than setting it to zero before quantization. This allows for quantum fluctuations in the torsion, with far reaching consequences.
