Effects of Twisted Noncommutativity in Multi-particle Hamiltonians

TL;DR

This paper explores how Drinfel'd twist-induced noncommutativity affects multi-particle Hamiltonians, revealing non-additive effects and novel features not seen in single-particle or traditional approaches.

Contribution

It demonstrates the implications of Drinfel'd twist on multi-particle Hamiltonians, highlighting non-additive effects and providing new insights into noncommutative quantum systems.

Findings

Non-additive effects in multi-particle Hamiltonians due to Drinfel'd twist

Recovery of noncommutative Quantum Hall Effect Hamiltonian

Illustration of twist effects on harmonic oscillator and configuration space quantization

Abstract

The noncommutativity induced by a Drinfel'd twist produces Bopp-shift like transformations for deformed operators. In a single-particle setting the Drinfel'd twist allows to recover the noncommutativity obtained from various methods which are not based on Hopf algebras. In multi-particle sector, on the other hand, the Drinfel'd twist implies novel features. In conventional approaches to noncommutativity, deformed primitive operators are postulated to act additively. A Drinfel'd twist implies non-additive effects which are controlled by the coproduct. We illustrate these features for a class of (abelian twist-deformed) 2D Hamiltonians. Suitable choices of the parameters lead to the Hamiltonian of the noncommutative Quantum Hall Effect, the harmonic oscillator, the quantization of the configuration space. The non-additive effects in the multi-particle sector, leading to results departing from the existing literature, are pointed out.