Calogero model revisited, commuting Hamiltonians, Hurwitz numbers

2022/11/10 by Orlov, A. Yu.
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2211.05923

Abstract

The generalized Mironov-Morozov-Natanson (MMN) equation includes a set of commuting operators, which can be considered as Hamiltonians for the quantum Calogero-Sutherland problem with a special value of the coupling constant (free fermion point). These Hamiltonians can be considered as the center of the enveloping algebra of the group GL_N(C). Another commuting series of Hamiltonians is presented, parametrized by an arbitrary matrix A∈ GL_N. These Hamiltonians are related to the Hurwitz numbers in the same way as in the case of the MMN equation and generate a generalized variant of the Calogero-Surtheland model.

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