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。 我研究了由此得到的粒子数近似定义的最佳可达到的精度。 标准的WKB假设在绝热参数中产生发散的渐进行列。 我推导出该序列中最佳项数的新公式，并证明最优截断的WKB序列的误差是指数级小的。 这种精度仍然不足以描述来自真空的粒子产生，这通常也是指数级小的。 通过微扰理论改进WKB假设可以获得足够精确的近似。 我定量地展示了在时变背景中粒子数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量。 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 the resulting approximate definition of the particle number. 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 from vacuum, 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 particle number 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.