Topological 2-Dimensional Quantum Mechanics
Alain Dasnieres de Veigy, Stephane Ouvry
TL;DR
This paper introduces a topological approach to 2D quantum mechanics using Chern-Simons theory, providing exact solutions, perturbative methods, and extensions to lattice and curved geometries.
Contribution
It develops a novel topological framework for 2D quantum systems, including exact N-body eigenstates and perturbative algorithms, expanding understanding of anyon models and curved spaces.
Findings
Derived exact N-body eigenstates for the model
Established a perturbative solution method
Extended analysis to particles on lattices and curved manifolds
Abstract
We define a Chern- Simons Lagrangian for a system of planar particles topologically interacting at a distance. The anyon model appears as a particular case where all the particles are identical. We propose exact N-body eigenstates, set up a perturbative algorithm, discuss the case where some particles are fixed on a lattice, and also consider curved manifolds. PACS numbers: 05.30.-d, 11.10.-z
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