标题： 标量场的福克量子化唯一性及宇宙学中度规符号变化过程 显示英文标题

标题： Uniqueness of the Fock quantization of scalar fields and processes with signature change in cosmology

摘要： 我们研究在非稳态时空（如宇宙学中出现的时空）中满足克莱因-戈登类型方程的标量场，假设所有相关的空间依赖性都包含在拉普拉斯算子中。 我们证明，如果采用结合准则（a）在场方程的空间对称性群下强制真空的不变性，以及（b）在量子理论中要求动力学的幺正实现，则场的描述---具有特定的正则对---以及场的福克表示确实以唯一的方式被确定（除了不改变物理预测的幺正变换）。 此外，我们将场方程解释为对应于一个共形静态宇宙时空中的标量场。 此外，在特权福克量子化中，我们研究了从双曲动力学区域到椭圆区域的物理状态演化的推广。 为了做到这一点，我们考虑场传播的时空中可能出现的度规符号变化的可能性，并讨论当变化发生时背景几何的行为，证明时空度规退化。 最后，我们认为这种类型的度规符号变化自然导致粒子产生现象，且具有指数级的生产率。 显示英文摘要

摘要： We study scalar fields subject to an equation of the Klein-Gordon type in nonstationary spacetimes, such as those found in cosmology, assuming that all the relevant spatial dependence is contained in the Laplacian. We show that the field description ---with a specific canonical pair--- and the Fock representation for the quantization of the field are fixed indeed in a unique way (except for unitary transformations that do not affect the physical predictions) if we adopt the combined criterion of (a) imposing the invariance of the vacuum under the group of spatial symmetries of the field equations and (b) requiring a unitary implementation of the dynamics in the quantum theory. Besides, we provide a spacetime interpretation of the field equations as those corresponding to a scalar field in a cosmological spacetime that is conformally ultrastatic. In addition, in the privileged Fock quantization, we investigate the generalization of the evolution of physical states from the hyperbolic dynamical regime to an elliptic regime. In order to do this, we contemplate the possibility of processes with signature change in the spacetime where the field propagates and discuss the behavior of the background geometry when the change happens, proving that the spacetime metric degenerates. Finally, we argue that this kind of signature change leads naturally to a phenomenon of particle creation, with exponential production.