Ren-integrable and ren-symmetric integrable systems

TL;DR

This paper introduces ren-symmetry, a new symmetry concept generalizing supersymmetry, and explores its implications for integrable systems, including the development of ren-integrable and ren-symmetric models with explicit examples.

Contribution

It proposes the novel concept of ren-symmetry, extending supersymmetry, and demonstrates its application in deriving new integrable systems like ren-KdV models.

Findings

Introduction of ren-symmetry as a generalization of supersymmetry

Derivation of new ren-integrable and ren-symmetric systems

Explicit examples of ren-KdV type equations

Abstract

A new type of symmetry, ren-symmetry describing anyon physics and the corresponding topological physics, is proposed. Ren-symmetry is a generalization of super-symmetry which is widely applied in super-symmetric physics such as the super-symmetric quantum mechanics, super-symmetric gravity, super-symmetric string theory, super-symmetric integrable systems and so on. The super-symmetry and Grassmann-number are, in some sense, the dual conceptions, which turns out that these conceptions coincide for the ren situation, that is, a similar conception of ren-number is devised to ren-symmetry. In particular, some basic results of the ren-number and ren-symmetry are exposed which allow one to derive, in principle, some new types of integrable systems including ren-integrable models and ren-symmetric integrable systems. Training examples of ren-integrable KdV type systems and ren-symmetric KdV equations are explicitly given.