Effects of twisted noncommutativity in multi-particle Hamiltonians

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.