Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model
Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model
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DOI：
10.1063/1.2167807
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发表时间：
2004-06
影响因子：
1.3
通讯作者：
E. Langmann
中科院分区：
文献类型：
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作者：
E. Langmann
我们提出了与椭圆型Calogero-Sutherland （eCS）系统相关的显著功能恒等式。我们从有限温度下圆周上任意子的量子场论模型中的eCS模型的第二次量子化中推导出它们。恒等式涉及两个具有任意和通常不同粒子数N和M的eCS哈密顿量，以及N+M变量的特定函数，作为N个粒子和M个反粒子的任意相关函数。除了得到具有相同统计参数λ的任意子的恒等式外，我们还得到了包含两个不同统计参数λ和1∕λ的任意子的“混合”相关函数的“对偶”关系。我们还通过直接计算给出了这些恒等式的替代的初等证明。
We present remarkable functional identities related to the elliptic Calogero-Sutherland (eCS) system. We derive them from a second quantization of the eCS model within a quantum field theory model of anyons on a circle and at finite temperature. The identities involve two eCS Hamiltonians with arbitrary and, in general, different particle numbers N and M, and a particular function of N+M variables arising as anyon correlation function of N particles and M antiparticles. In addition to identities obtained from anyons with the same statistics parameter λ, we also obtain “dual” relations involving “mixed” correlation functions of anyons with two different statistics parameters λ and 1∕λ. We also give alternative, elementary proofs of these identities by direct computations.