标题： 二维稀疏引力约化相空间的量子化 显示英文标题

标题： Quantization of the Reduced Phase Space of Two-Dimensional Dilaton Gravity

摘要： 我们使用偏微分方程的正式理论来研究一些二维稀疏引力模型。 这使我们能够证明约化相空间是二维的，而无需显式构造。 通过使用方便的（静态）规范，我们将理论简化为耦合的\ode ，并且能够为一些感兴趣的势能推导出闭合形式的解。 我们使用有效的（粒子）拉格朗日量来处理约化场方程，以便在有限维设置中对系统进行量子化，从而得到一个精确的偏微分 Wheeler-DeWitt 方程，而不是泛函方程。 计算了一些量子态的 WKB 近似，并与经典哈密顿-雅可比理论进行了比较。 检查了最小耦合物质的影响。 显示英文摘要

摘要： We study some two-dimensional dilaton gravity models using the formal theory of partial differential equations. This allows us to prove that the reduced phase space is two-dimensional without an explicit construction. By using a convenient (static) gauge we reduce the theory to coupled \ode s and we are able to derive for some potentials of interest closed-form solutions. We use an effective (particle) Lagrangian for the reduced field equations in order to quantize the system in a finite-dimensional setting leading to an exact partial differential Wheeler-DeWitt equation instead of a functional one. A WKB approximation for some quantum states is computed and compared with the classical Hamilton-Jacobi theory. The effect of minimally coupled matter is examined.