新变量下CGHS模型的局部真哈密顿量
A local true Hamiltonian for the CGHS model in new variables
摘要：
在前人工作的基础上，给出了CGHS模型在新变量下的完全经典解。我们对一类耦合到物质的二维双光子引力系统进行了一系列的分析和变换，得到了新变量下的CGHS哈密顿量。这给了我们一个第二类系统，一个由一个哈密尔顿约束、一个同构约束和两个第二类约束组成的全哈密尔顿算子。我们计算了Dirac括号，通过引入一个新的变量，使它们成为一个类似于泊松括号的标准形式。然后，通过重新标度lapse和shift，将Hamilton约束转化为与自身具有强Abel代数的形式。这一性质在真空和物质耦合的情况下都成立。然后，对于真空和耦合到物质的每一种情况，我们预制两个规范固定，每种情况一套，并在两种情况下完全解决经典系统。耦合到物质的情况下的规范固定是通过实施一种方法的基础上的正则变换到一组新的变量，并导致一个真正的本地哈密顿量。我们还表明，我们的形式主义是一致的，与原来的CGHS文件显示，在这两种情况下的运动方程是相同的。最后我们导出了模型的相关表面项。
英文摘要：
Following our previous work, a complete classical solution of the CGHS model in Hamiltonian formulation in new variables is given. We preform a series of analyses and transformations to get to the CGHS Hamiltonian in new variables from a generic class of two dimensional dilatonic gravitational systems coupled to matter. This gives us a second class system, a total Hamiltonian consisting of a Hamiltonian constraint, a diffeomorphism constraint and two second class constraints. We calculate the Dirac brackets, bring them to a standard form similar to the Poisson brackets by introducing a new variable. Then by rescaling lapse and shift, the Hamiltonian constraint is transformed into a form where it has an strong Abelian algebra with itself. This property holds both in vacuum case and in case with matter coupling. Then for each of the vacuum and the coupled-to-matter cases, we preform two gauge fixings, one set for each case, and solve the classical system completely in both cases. The gauge fixing of the case coupled to matter is done by implementing a method based on canonical transformation to a new set of variables and leads to a true local Hamiltonian. We also show that our formalism is consistent with the original CGHS paper by showing that the equations of motion are the same in both cases. Finally we derive the relevant surface term of the model.
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