论文标题
Bianchi VIII Wheeler DeWitt方程和领先的订单解决方案的新解决方案，用于$λ$ $ $ \ ne $ 0和一个原始磁场
New Solutions To The Bianchi VIII Wheeler DeWitt Equation And Leading Order Solutions For $Λ$ $\ne$ 0 And A Primordial Magnetic Field
论文作者
论文摘要
使用Euclidean-Sign-Sign Emi-Semagical Classical Classical Metsical获得了针对Lorentzian签名对称对称性的降低的bianchi VIII Wheeler DeWitt方程。使用上述方法，我们为Bianchi VIII波函数定义了“激发”状态，并构造了似乎是散射和结合状态的混合物的领先顺序“激发”状态。还提出了$λ\ ne 0 $ bianchi viii欧几里得签名汉密尔顿雅各比方程的六个新解决方案，可用于构建与Lorentzian Signature Symmetraly Symmetry Symmetry降低Wheeler DeWitt方程相对应的半经典状态。此外，当存在$λ\ ne 0 $和一个对齐的原始磁场时，发现了Bianchi VIII模型的Euclidean-Signature Hamilton jacobi方程的新解决方案。此外，我们在不存在物质的情况下找到了欧几里得 - 签名汉密尔顿雅各布方程的八种新的复杂解决方案，可用于构建其他半古典状态。我们还研究了上述溶液仅限于$β+$轴时的领先顺序波函数。在介绍这些结果之前，我们解释了欧几里得 - 签名半古典方法，并讨论如何求解所得方程，当将其应用于洛伦兹 - 签名对称性降低Bianchi Viii Wheeler DeWitt方程时，该方法会生成。此处使用的欧几里得 - 签名半古典方法也适用于其他现场理论。在本文中介绍的工作进一步显示了欧克利德 - 签名的半古典方法，用于解决量子宇宙学和解决洛伦兹的标志性问题的问题。
New non trivial solutions to the Lorentzian-signature symmetry reduced Bianchi VIII Wheeler DeWitt equation for Hartle Hawking ordering parameters $ \pm 2\sqrt{33} $ are obtained using an Euclidean-signature semi classical method. Using the aforementioned method we define 'excited' states for the Bianchi VIII wave function and construct leading order 'excited' states which appear to be a hybrid of scattering and bound states. Also six new solutions for the $Λ\ne 0$ Bianchi VIII Euclidean-signature Hamilton Jacobi equation are presented which can be used to construct semi-classical states corresponding to the Lorentzian signature symmetry reduced Wheeler DeWitt equation. In addition, new solutions to the Euclidean-signature Hamilton Jacobi equation for the Bianchi VIII models are found when $Λ\ne 0$ and an aligned primordial magnetic field is present. Furthermore, we find eight new complex solutions to the Euclidean-signature Hamilton Jacobi equation for the case when matter is not present, which can be used to construct additional semi-classical states. We also study the leading order wave functions which result from our aforementioned solutions when they are restricted to the $β+$ axis. Prior to presenting these results we explain the Euclidean-signature semi classical method and discuss how to solve the resultant equations this method generates when it is applied to the Lorentzian-signature symmetry reduced Bianchi VIII Wheeler DeWitt equation. The Euclidean-signature semi-classical method used here is applicable to other field theories as well. The work presented throughout this paper further shows the power Eulclidean-signature semi classical methods possess for solving problems in quantum cosmology and solving Lorentzian signature problems in general.
