标题： 三维电磁pp波时空的经典和量子分析 显示英文标题

标题： Classical and quantum analysis of 3D electromagnetic pp-wave spacetime

摘要： 三维电磁pp波时空的一般经典解已经获得。 相关的线元包含一个任意的基本函数，提供了无限多个非等价几何作为解。 基于对称群进行了分类。 据我们所知，只有其中一类的解是已知的。 一些类的动力学也从一个构造出来的极小超空间拉格朗日量中推导出来。 这个拉格朗日量包含一个自由度（时间位移），可以视为动力学或非动力学的（分别表示奇异或正则的拉格朗日量）。 令人惊讶的是，在经典解的空间上，可以建立这两种观点的等价性。 然后使用规范量子化来对奇异和正则哈密顿量进行系统量子化。 对量子态的后续解释基于一种类似玻姆的分析。 半经典轨迹仅在正则哈密顿量下以及特别在本征态的叠加情况下（使用了一个高斯初始状态）偏离经典轨迹。 因此，上述等价性在量子层面上被打破。 值得注意的是，在初始波包广泛展开的极限情况下，半经典轨迹趋于经典轨迹。 因此，即使使用这种简单的叠加态，经典解也可以作为半经典的极限获得。 显示英文摘要

摘要： The general classical solution of the 3D electromagnetic pp-wave spacetime has been obtained. The relevant line element contains an arbitrary essential function providing an infinite number of in-equivalent geometries as solutions. A classification is presented based on the symmetry group. To the best of our knowledge, the solution corresponding to only one of the Classes is known. The dynamics of some of the Classes was also derived from a minisuperspace Lagrangian which has been constructed. This Lagrangian contains a degree of freedom (the lapse) which can be considered either as dynamical or non-dynamical (indicating a singular or a regular Lagrangian correspondingly). Surprisingly enough, on the space of classical solutions, an equivalence of these two points of view can be established. The canonical quantization is then used in order to quantize the system for both the singular and regular Hamiltonian. A subsequent interpretation of quantum states is based on a Bohm-like analysis. The semi-classical trajectories deviate from the classical only for the regular Hamiltonian and in particular for a superposition of eigenstates (a Gaussian initial state has been used). Thus, the above mentioned equivalence is broken at the quantum level. It is noteworthy that the semi-classical trajectories tend to the classical ones in the limit where the initial wavepacket is widely spread. Hence, even with this simple superposition state, the classical solutions are acquired as a limit of the semi-classical.