论文标题
Ramanujan总结和Casimir效应
Ramanujan summation and the Casimir effect
论文作者
论文摘要
斯里尼瓦萨·拉马努扬（Srinivasa Ramanujan）是一位伟大的自学成才的印度数学家，他在一个世纪前去世，享年32岁，享年32岁，一年后从英格兰返回。在他的众多成就中，有限的有限值分配给Divergent系列，这与Riemann的$ζ$ function相对应。他几乎没有给出任何解释，但是遵循他给出的一些提示，我们基于分析延续为最著名的例子建立了一个直接的理由。作为Ramanujan求和的物理应用，我们讨论了Casimir效应，其中消除发散项的这种方式对应于真空能密度的重新归一化，特别是光子场的重新归一化。这导致了导电板之间Casimir力的预测，这已经通过实验准确地证实。最后，我们回顾了有关卡西米尔效应的含义和解释的讨论。这将我们带到了深色能量大小的奥秘。
Srinivasa Ramanujan was a great self-taught Indian mathematician, who died a century ago, at the age of only 32, one year after returning from England. Among his numerous achievements is the assignment of sensible, finite values to divergent series, which correspond to Riemann's $ζ$-function with negative integer arguments. He hardly left any explanation about it, but following the few hints that he gave, we construct a direct justification for the best known example, based on analytic continuation. As a physical application of Ramanujan summation we discuss the Casimir effect, where this way of removing a divergent term corresponds to the renormalization of the vacuum energy density, in particular of the photon field. This leads to the prediction of the Casimir force between conducting plates, which has now been accurately confirmed by experiments. Finally we review the discussion about the meaning and interpretation of the Casimir effect. This takes us to the mystery surrounding the magnitude of Dark Energy.
