玻色子服从玻色-爱因斯坦分布吗？--詹蒂莱分布的两个迭代极限
Do bosons obey Bose-Einstein distribution: two iterated limits of Gentile distribution
摘要：
人们普遍认为，只要把玻色子的最大占有数设为无穷大，这是玻色子不可分解的要求，就可以得到玻色子服从的统计分布--玻色-爱因斯坦分布。然而，在这封信中，我们表明，只有无限大的最大占有数不能唯一地实现玻色-爱因斯坦分布，因为在推导玻色-爱因斯坦分布时，遇到了迭代极限的问题。为了得到玻色-爱因斯坦分布，我们需要把最大占有数和粒子总数都取为无穷大，然后，取极限的顺序问题就出现了。极限运算的不同顺序将导致不同的统计分布。为了实现玻色-爱因斯坦分布，除了设置最大占用数外，我们还需要说明极限运算的顺序。
英文摘要：
It is a common impression that by only setting the maximum occupation number to infinity, which is the demand of the indistinguishability of bosons, one can achieve the statistical distribution that bosons obey -- the Bose-Einstein distribution. In this letter, however, we show that only with an infinite maximum occupation number one cannot uniquely achieve the Bose-Einstein distribution, since in the derivation of the Bose-Einstein distribution, the problem of iterated limit is encountered. For achieving the Bose-Einstein distribution, one needs to take both the maximum occupation number and the total number of particles to infinities, and, then, the problem of the order of taking limits arises. Different orders of the limit operations will lead to different statistical distributions. For achieving the Bose-Einstein distribution, besides setting the maximum occupation number, we also need to state the order of the limit operations.
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