复杂的能量和时间的开始提出了散射和衰变的理论
Complex Energies and Beginnings of Time Suggest a Theory of Scattering and Decay
摘要：
散射和衰变的量子理论中有许多有用的概念（如李普曼-施温格群、纯输出边界条件、指数衰减的伽莫夫向量、因果关系）在量子力学的传统（希尔伯特空间）公理所设定的数学框架中并没有得到很好的定义。以李普曼-施温格方程为出发点，以共振和衰变统一的理论为目标，我们猜想了一个新的量子力学公理，它在数学上区分了预备态和检测到的观测值。根据李普曼-施温格方程的两个符号$\pm iε$，这个公理用两个哈代空间代替了传统量子力学的一个希尔伯特空间。新的Hardy空间理论自动地提供了从$S$ -矩阵的复数极点导出的具有指数时间演化的Gamow kets。它解决了因果关系问题，因为它导致了半群的演化。但是这个半群给量子物理学带来了一个新的概念，即半群时间$t=0$，时间的开始。最后一节讨论了它的解释和观察结果。
英文摘要：
Many useful concepts for a quantum theory of scattering and decay (like Lippmann-Schwinger kets, purely outgoing boundary conditions, exponentially decaying Gamow vectors, causality) are not well defined in the mathematical frame set by the conventional (Hilbert space) axioms of quantum mechanics. Using the Lippmann-Schwinger equations as the takeoff point and aiming for a theory that unites resonances and decay, we conjecture a new axiom for quantum mechanics that distinguishes mathematically between prepared states and detected observables. Suggested by the two signs $\pm iε$ of the Lippmann-Schwinger equations, this axiom replaces the one Hilbert space of conventional quantum mechanics by two Hardy spaces. The new Hardy space theory automatically provides Gamow kets with exponential time evolution derived from the complex poles of the $S$-matrix. It solves the causality problem since it results in a semigroup evolution. But this semigroup brings into quantum physics a new concept of the semigroup time $t=0$, a beginning of time. Its interpretation and observations are discussed in the last section.
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