Many-Body Wigner Quantum Systems

TL;DR

This paper introduces many-body Wigner quantum systems with noncanonical operators, revealing a finite, equidistant energy spectrum, noncommutative geometry, and exclusion statistics, expanding the understanding of quantum many-body models.

Contribution

It presents new examples of many-body Wigner quantum systems with unique spectral and geometric properties, including noncanonical operators and noncommutative geometry.

Findings

Energy spectrum is finite and equidistant.

System exhibits noncommutative geometry within a small volume.

Underlying statistics is exclusion statistics.

Abstract

We present examples of many-body Wigner quantum systems. The position and the momentum operators ${\bf R}_A$ and ${\bf P}_A,\; A=1,\ldots,n+1$, of the particles are noncanonical and are chosen so that the Heisenberg and the Hamiltonian equations are identical. The spectrum of the energy with respect to the centre of mass is equidistant and has finite number of energy levels. The composite system is spread in a small volume around the centre of mass and within it the geometry is noncommutative. The underlying statistics is an exclusion statistics.