论文标题
使用分隔的差异的戴森系列的无整体表示
An integral-free representation of the Dyson series using divided differences
论文作者
论文摘要
Dyson系列是多维时级积分的无限总和，它是交互作用图中量子时间进化运算符的形式表示。使用划分差异的数学工具，我们引入了该系列的替代表示形式，该表示完全没有时间顺序和积分。在这种新的形式主义中，给出了dyson的扩展为指数函数的有效分配差异的总和，从而大大简化了Dyson扩展项的计算，同时还允许在Schr {Ö} dinger-dinger-picture中直接执行时间依赖性的扰动计算。我们通过研究多种用例来展示这种新型表示的实用性。我们还讨论了几个即时申请。
The Dyson series is an infinite sum of multi-dimensional time-ordered integrals, which serves as a formal representation of the quantum time-evolution operator in the interaction-picture. Using the mathematical tool of divided differences, we introduce an alternative representation for the series that is entirely free from both time ordering and integrals. In this new formalism, the Dyson expansion is given as a sum of efficiently-computable divided differences of the exponential function, considerably simplifying the calculation of the Dyson expansion terms, while also allowing for time-dependent perturbation calculations to be performed directly in the Schr{ö}dinger-picture. We showcase the utility of this novel representation by studying a number of use cases. We also discuss several immediate applications.
