Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model
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arXiv
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| Format: | Preprint |
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2004
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| _version_ | 1866916589200211968 |
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| author | Langmann, Edwin |
| author_facet | Langmann, Edwin |
| contents | We present further 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 $M$ anti-particles. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_math_ph_0406061 |
| institution | arXiv |
| publishDate | 2004 |
| record_format | arxiv |
| spellingShingle | Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model Langmann, Edwin Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems 35Q58, 81T40 We present further 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 $M$ anti-particles. 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. |
| title | Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model |
| topic | Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems 35Q58, 81T40 |
| url | https://arxiv.org/abs/math-ph/0406061 |