（1+1）维Hokava-Lifshitz引力理论的量子化
Quantization of (1+1)-dimensional Hořava-Lifshitz theory of gravity
摘要：
本文研究了（1+1）维可投射的Hohava-Lifshitz（HL）引力的量子化，发现当只存在引力时，系统可以按照正则Dirac量子化进行量子化，并且相应的波函数对于某些算符的序是可正规化的.相应的哈密顿量也可以用简谐振子来表示，由此量子化可以用标准的量子力学方法来进行。当HL引力最小耦合到一个标量场时，动量约束在基本变量仅为时间函数的情况下得到了显式求解。在这种情况下，耦合系统也可以通过狄拉克过程量子化，并且相应的波函数也可以对某些特定的算符排序进行归一化。哈密顿量也可以用两个相互作用的谐振子来表示。但是，当相互作用关闭时，其中一个谐振子具有正能量，而另一个具有负能量。一个显着的特点是，从一个经典的汉密尔顿到一个量子力学的运营商的顺序发挥了根本性的作用，以惠勒-德维特方程有非平凡的解决方案。此外，时空是量子化的，即使它是经典奇异的。
英文摘要：
In this paper, we study the quantization of the (1+1)-dimensional projectable Hořava-Lifshitz (HL) gravity, and find that, when only gravity is present, the system can be quantized by following the canonical Dirac quantization, and the corresponding wavefunction is normalizable for some orderings of the operators. The corresponding Hamilton can also be written in terms of a simple harmonic oscillator, whereby the quantization can be carried out quantum mechanically in the standard way. When the HL gravity minimally couples to a scalar field, the momentum constraint is solved explicitly in the case where the fundamental variables are functions of time only. In this case, the coupled system can also be quantized by following the Dirac process, and the corresponding wavefunction is also normalizable for some particular orderings of the operators. The Hamilton can be also written in terms of two interacting harmonic oscillators. But, when the interaction is turned off, one of the harmonic oscillators has positive energy, while the other has negative energy. A remarkable feature is that orderings of the operators from a classical Hamilton to a quantum mechanical one play a fundamental role in order for the Wheeler-DeWitt equation to have nontrivial solutions. In addition, the space-time is well quantized, even when it is classically singular.
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