标题： 宇宙学粒子产生与WKB近似的精度 显示英文标题

标题： Cosmological particle production and the precision of the WKB approximation

摘要： 由缓慢变化的引力场产生的粒子通常使用弯曲时空中的量子场论来描述。 计算需要真空态的定义，这可以通过绝热（WKB）近似给出。 我研究了这种绝热真空近似定义的最佳可达到精度。 标准的WKB假设在绝热参数中产生发散的渐进行列。 我推导出了该序列中最佳项数的新公式，并证明了最优截断的WKB序列的误差是指数级小的。 这种精度仍然不足以描述粒子产生，这通常是指数级小的。 通过微扰理论改进WKB假设可以找到足够精确的近似。 我定量地表明，在时变背景中真空定义的基本不可避免的不精确性等于该时期预期发生的粒子产生。 结果通过解析和数值例子进行了说明。 显示英文摘要

摘要： Particle production by slow-changing gravitational fields is usually described using quantum field theory in curved spacetime. Calculations require a definition of the vacuum state, which can be given using the adiabatic (WKB) approximation. I investigate the best attainable precision of this approximate definition of the adiabatic vacuum. The standard WKB ansatz yields a divergent asymptotic series in the adiabatic parameter. I derive a novel formula for the optimal number of terms in that series and demonstrate that the error of the optimally truncated WKB series is exponentially small. This precision is still insufficient to describe particle production, which is typically also exponentially small. An adequately precise approximation can be found by improving the WKB ansatz through perturbation theory. I show quantitatively that the fundamentally unavoidable imprecision in the definition of vacuum in a time-dependent background is equal to the particle production expected to occur during that epoch. The results are illustrated by analytic and numerical examples.