Finite-temperature form factors in the free Majorana theory
Finite-temperature form factors in the free Majorana theory
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自由马约拉纳理论中的有限温度形状因子
DOI：
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发表时间：
2005
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通讯作者：
B. Doyon
中科院分区：
文献类型：
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作者：
B. Doyon
本文研究了有限温度下自由质量马约拉纳理论中相关函数的大距离展开，即圆柱上零磁场下的伊辛场论。我们开发了一种模拟零温度相关函数的光谱分解或形状因子展开的方法，引入了“有限温度形状因子”的概念。我们的技术与以往在这个课题上的尝试有所不同。我们证明了有限温度形式因子的适当解析延拓给出了量化方案在圆上的形式因子。我们证明了有限温度的形状因子扩展能够在圆上复制形状因子的扩展。我们计算了非相互作用场（相对于基本费米子场的局部场）的有限温度形状因子。我们观察到，它们是由它们的零温度形状因子和其他低尺度领域的形状因子混合而成的。然后，我们计算了有序场和无序场的有限温度形式因子。为此，我们导出了Riemann-Hilbert问题，该问题完全规定了一般扭转场（有序场和无序场及其子类）的有限温度形式因子集。这个黎曼-希尔伯特问题不同于零温度问题，它的解也不同。我们的结果与已知的有序场和无序场圆上的形状因子一致。
We study the large distance expansion of correlation functions in the free massive Majorana theory at finite temperature, alias the Ising field theory at zero magnetic field on a cylinder. We develop a method that mimics the spectral decomposition, or form factor expansion, of zero-temperature correlation functions, introducing the concept of ‘finite-temperature form factors’. Our techniques are different from those of previous attempts in this subject. We show that an appropriate analytical continuation of finite-temperature form factors gives form factors in the quantization scheme on the circle. We show that finite-temperature form factor expansions are able to reproduce expansions in form factors on the circle. We calculate finite-temperature form factors of non-interacting fields (fields that are local with respect to the fundamental fermion field). We observe that they are given by a mixing of their zero-temperature form factors and of those of other fields of lower scaling dimension. We then calculate finite-temperature form factors of order and disorder fields. For this purpose, we derive the Riemann–Hilbert problem that completely specifies the set of finite-temperature form factors of general twist fields (order and disorder fields and their descendants). This Riemann–Hilbert problem is different from the zero-temperature one, and so are its solutions. Our results agree with the known form factors on the circle of order and disorder fields.