论文标题
具有粒子创造和紫外线截止的多时间Schrodinger方程的一致性证明
Consistency Proof for Multi-Time Schrodinger Equations with Particle Creation and Ultraviolet Cut-Off
论文作者
论文摘要
对于多时间波函数，自然而然地作为量子状态矢量的相对论粒子位点表示，schrödinger方程的类似物由几个方程组成，每个方程式是一个时变量。这导致了如何证明这种PDE系统一致性的问题。对于通过粒子创建的理论而言，这个问题变得更加困难，因为波浪函数的不同扇区具有不同的时间变量。 Petrat and Tumulka（2014）以其一致性为例，以这种模型为例和不合格的论点。在将紫外线截止的创建和歼灭术语中引入了多个时间演化方程式之后，我们在这里给这里提供了严格的论点版本。这些方程式形成了无限的耦合PDES系统；它们基于狄拉克方程，但并非完全相对论（部分是由于截止者）。我们证明了从某个类别的每个初始波函数中的平滑解决方案的存在和唯一性，该类别与适当的希尔伯特空间中的密集子空间相对应。
For multi-time wave functions, which naturally arise as the relativistic particle-position representation of the quantum state vector, the analog of the Schrödinger equation consists of several equations, one for each time variable. This leads to the question of how to prove the consistency of such a system of PDEs. The question becomes more difficult for theories with particle creation, as then different sectors of the wave function have different numbers of time variables. Petrat and Tumulka (2014) gave an example of such a model and a non-rigorous argument for its consistency. We give here a rigorous version of the argument after introducing an ultraviolet cut-off into the creation and annihilation terms of the multi-time evolution equations. These equations form an infinite system of coupled PDEs; they are based on the Dirac equation but are not fully relativistic (in part because of the cut-off). We prove the existence and uniqueness of a smooth solution to this system for every initial wave function from a certain class that corresponds to a dense subspace in the appropriate Hilbert space.
