New approach to ${\cal N} {=}2$ supersymmetric Ruijsenaars-Schneider model

TL;DR

This paper introduces a simplified formulation of supercharges and Hamiltonian for ${ m N}=2$ supersymmetric Ruijsenaars-Schneider models across three interaction types, streamlining their mathematical structure.

Contribution

It provides a new, simplified expression for supercharges and Hamiltonian in ${ m N}=2$ supersymmetric Ruijsenaars-Schneider models for three interaction cases.

Findings

Simplified supercharges and Hamiltonian expressions for three interaction types.

Unified rational function form depending on fermionic bilinears.

Enhanced understanding of supersymmetric extensions in integrable models.

Abstract

We present a very simple form of the supercharges and the Hamiltonian of ${\cal N} {=}\,2$ supersymmetric extension of $n$-particle Ruijsenaars--Schneider models for three cases of the interaction: $1/(x_i-x_j)$, $1/tan(x_i-x_j)$, $1/tanh(x_i-x_j)$. The long "fermionic tails" of the supercharges and Hamiltonian rolled up in the simple rational functions depending on fermionic bilinears.