论文标题
Bianchi II和VII $ _ {H = 0} $通过Euclidean-Signature半经典方法重新审视的模型
Bianchi II and VII$_{h=0}$ Models Revisited Via The Euclidean-Signature Semi Classical Method
论文作者
论文摘要
我们以新颖的方式应用了一种修改的半古典方法，将当存在宇宙常数，对齐的电磁场和僵硬物质时，将Bianchi II和VII $ _ {H = 0} $模型应用于VII $ _ {H = 0} $。此外，当包括对齐的电磁场时，我们研究了非共同量子比安奇II模型。通过使用Euclidean-Signature半古典方法，我们找到了这些模型相应的Lorentzian签名Wheeler DeWitt方程的新解决方案，我们可以定性地解释。这些涉及物质源的上述模型的新解决方案揭示了一些潜在的有趣效果，这些效果应作为可能的现象进行编年史，以至于量子重力的玩具模型可以诱导量子宇宙的演变。此外，我们发现“激发”状态与以前使用这种方法发现的Bianchi IX和Taub模型的“激发”状态不同。通过比较和对比这些模型给出的“激发”状态，我们有助于更好地低估构成Wheeler DeWitt方程的“激发”状态解决方案。我们的结果进一步表明了欧几里得 - 签名半经典方法的实用性，即无需调用灯芯旋转即可解决洛伦兹的签名问题。这种不需要应用灯芯旋转的功能使得该方法可能非常有用，可用于解决骨相对论场理论和量子重力中的各种问题。
We apply in a novel fashion a modified semi-classical method to the Bianchi II and VII$_{h=0}$ models when a cosmological constant, aligned electromagnetic field and stiff matter are present. Additionally we study the non-commutative quantum Bianchi II models when an aligned electromagnetic field is included. Through the use of the Euclidean-signature semi classical method we find a plethora of new solutions to these model's corresponding Lorentzian signature Wheeler DeWitt equations which we can interpret qualitatively. These new solutions for the aforementioned models involving matter sources reveal some potentially interesting effects that should be chronicled as possible phenomena that a toy model of quantum gravity can induce on the evolution of a quantum universe. Furthermore we find 'excited' states which behave differently from the 'excited' states of the Bianchi IX and Taub models that were previously uncovered using this method. By comparing and contrasting the 'excited' states given by these models we help facilitate a better understating of what constitutes an 'excited' state solution of the Wheeler Dewitt equation. Our results further show the utility of the Euclidean-signature semi classical method for tackling Lorentzian signature problems without having to invoke a Wick rotation. This feature of not needing to apply a Wick rotation makes this method potentially very useful for tackling a variety of problems in bosonic relativistic field theory and quantum gravity.
