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Supersymmetric Ruijsenaars-Schneider model.

O Blondeau-Fournier1, P Desrosiers1,2, P Mathieu1

  • 1Département de physique, de génie physique et d'optique, Université Laval, Québec, Canada G1V 0A6.

Physical Review Letters
|April 11, 2015
PubMed
Summary
This summary is machine-generated.

We present a new supersymmetric model, a generalization of the trigonometric Ruijsenaars-Schneider model, incorporating super Poincaré symmetry. Its Hamiltonian is diagonalized by Macdonald superpolynomials, leading to a discrete Hilbert space.

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Area of Science:

  • Mathematical Physics
  • Quantum Field Theory
  • Supersymmetry

Background:

  • The trigonometric Ruijsenaars-Schneider model is a classical integrable system with applications in mathematical physics.
  • Supersymmetric generalizations are crucial for understanding quantum field theories and string theory.
  • Macdonald superpolynomials are a recent development in the study of special functions and integrable systems.

Purpose of the Study:

  • To introduce an integrable supersymmetric generalization of the trigonometric Ruijsenaars-Schneider model.
  • To investigate the symmetry algebra and Hamiltonian of this new model.
  • To explore the implications of the model's consistency on its Hilbert space structure.

Main Methods:

  • Construction of a supersymmetric extension of the trigonometric Ruijsenaars-Schneider model.
  • Analysis of the model's symmetry algebra, including the super Poincaré algebra.
  • Diagonalization of the Hamiltonian using Macdonald superpolynomials.
  • Investigation of the scalar product's consistency conditions.

Main Results:

  • An integrable supersymmetric generalization of the trigonometric Ruijsenaars-Schneider model is successfully constructed.
  • The symmetry algebra of the model incorporates the super Poincaré algebra.
  • The Hamiltonian is diagonalized by Macdonald superpolynomials.
  • The consistency of the scalar product necessitates a discrete Hilbert space.

Conclusions:

  • The presented model offers a novel framework for studying integrable systems with supersymmetry.
  • The use of Macdonald superpolynomials provides a powerful tool for analyzing such models.
  • The discreteness of the Hilbert space is a significant finding with potential implications for quantum mechanics and related fields.