Application of the Mathematical Methods of the Braid Group Theory to Quantization of Many-Particle Systems

doi:https://doi.org/10.12693/aphyspola.85.483

Open AccessArticle10.12693/aphyspola.85.483

Application of the Mathematical Methods of the Braid Group Theory to Quantization of Many-Particle Systems

Dorota Jacak,Lucjan Jacak,Konrad Wieczorek-1994-03-01-Acta Physica Polonica A

TL;DRAbstract

The problem of the non-standard statistics for one-, two-and three--dimensional systems of N identical particles on various manifolds is reviewed in terms of the braid group theory. The braid groups together with their unitary representations are studied for the line, circle, plane, sphere, torus and the three-dimensional Euclidean space. Nonequivalent quantizations of several physical systems are presented.

Chat with Paper

AI Agents for this Paper

The problem of the non-standard statistics for one-, two-and three--dimensional systems of N identical particles on various manifolds is reviewed in terms of the braid group theory. The braid groups together with their unitary representations are studied for the line, circle, plane, sphere, torus and the three-dimensional Euclidean space. Nonequivalent quantizations of several physical systems are presented.

Keywords

BraidBraid groupQuantization (signal processing)Group theoryGroup (periodic table)Algebra over a fieldTheoretical physicsMathematics

Chat

Click to start Chat