Physics NotePublished
Effects of Twisted Noncommutativity\\ in Multi-particle Hamiltonians
F. Toppan
Publication details
- Authors
- F. Toppan
- Type
- Physics Note
- Status
- Published
- Publication date
- 07/02/2013
- Description
- 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.
- Year
- 2012
- Number
- CBPF-NF-013/12
- Linked to a thesis
- No
- Linked to a grant
- No