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Gauge momentum operators for the Calogero-Sutherland model with anti-periodic boundary condition

Arindam Chakraborty·Subhankar Ray·J. Shamanna
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Abstract

The integrability of a classical Calogero systems with anti-periodic boundary condition is studied. This system is equivalent to the periodic model in the presence of a magnetic field. Gauge momentum operators for the anti-periodic Calogero system are constructed. These operators are hermitian and simultaneously diagonalizable with the Hamiltonian. A general scheme for constructing such momentum operators for trigonometric and hyperbolic Calogero-Sutherland model is proposed. The scheme is applicable for both periodic and anti-periodic boundary conditions. The existence of these momentum operators ensures the integrability of the system. The interaction parameter $λ$ is restricted to a certain subset of real numbers. This restriction is in fact essential for the construction of the hermitian gauge momentum operators.

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Arindam Chakraborty, Subhankar Ray, J. Shamanna. 2007-01-15. Gauge momentum operators for the Calogero-Sutherland model with anti-periodic boundary condition. https://arxiv.org/abs/hep-th/0607108

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