论文标题
Casimir自由能的大规模费米斯：各种方法的比较研究
Casimir free energy for massive fermions: a comparative study of various approaches
论文作者
论文摘要
我们使用三种不同的一般方法和每个针对每种的显式溶液计算两个平行板之间的大量费米片场的Casimir热力学量。 Casimir热力学量包括Casimir Helmholtz自由能，压力，能量和熵。我们使用的三种一般方法基于Casimir热力学量的基本定义，ZETA函数方法表示的分析延续方法和零温度减法方法。我们还包括后两种方法的重新归一化版本，而第一种方法不需要一种方法。在每种一般方法中，我们以几种不同的方式获得相同的结果来确定所选的无限次数的取消。然后，我们对三种不同的一般方法及其结果进行比较研究，并表明它们原则上不等于彼此，并且它们通常会产生不同的结果。特别是，我们表明，仅通过第一种方法计算得出的CASIMIR热力学量具有所有三个特性，即作为温度，场的质量或板之间的距离增加。
We compute the Casimir thermodynamic quantities for a massive fermion field between two parallel plates with the MIT boundary conditions, using three different general approaches and present explicit solutions for each. The Casimir thermodynamic quantities include the Casimir Helmholtz free energy, pressure, energy and entropy. The three general approaches that we use are based on the fundamental definition of Casimir thermodynamic quantities, the analytic continuation method represented by the zeta function method, and the zero temperature subtraction method. We include the renormalized versions of the latter two approaches as well, whereas the first approach does not require one. Within each general approach, we obtain the same results in a few different ways to ascertain the selected cancellations of infinities have been done correctly. We then do a comparative study of the three different general approaches and their results, and show that they are in principle not equivalent to each other and they yield, in general, different results. In particular, we show that the Casimir thermodynamic quantities calculated only by the first approach have all three properties of going to zero as the temperature, the mass of the field, or the distance between the plates increases.
