The quantum Hall effect occurs when a conductor carrying a current is placed in a perpendicular magnetic field. If certain conditions are met, such as strong magnetic field and low temperature, the resistivity becomes quantised, taking values of integer or fractional multiples of h/e2. By analysing the movement of electrons in a magnetic field classically and quantum mechanically information about the integer quantum Hall effect and the fractional quantum Hall effect can be gathered, using the two different gauge potentials of Landau gauge and Symmetric gauge. Resistance Metrology is one field of study that the quantum Hall effect has greatly impacted by providing a way to universally maintain the ohm, with significantly less uncertainty than previously. / Den kvantmekaniska hall-effekten uppstår när en strömbärande ledare placeras i ett vinkelrätt magnetfält. Om vissa villkor är uppfyllda, såsom starkt magnetfält och låg temperatur, blir resistiviteten kvantiserad. Given av heltal (integer) eller fraktions-(fractional) multiplar av h/e2. Genom att analysera elektroners rörelse i ett magnetfält klassiskt och kvantmekaniskt fås information om Hall-effekterna; integer quantum Hall effect och fractional quantum Hall effect, med hjälp av de två gauge potentialerna Landau gauge och Symmetrisk gauge. Resistansmetrologi är ett forskningsområde som kvant Hall-effekten har starkt påverkat genom att tillhandahålla ett sätt att universellt upprätthålla ohm-enheten med betydligt mindre osäkerhet än tidigare.

This thesis deals with a conformal field theoretical treatment of abelian anyons in (1 + 1)-dimensions and their relation to the integrable Calogero-Sutherland models. We generalize previous work relating anyons to the Calogero-Sutherland model by showing that the correlation function of the anyon field operators corresponds to the eigenfunctions of the deformed Calogero-Sutherland model. Our results suggest a physical application of the deformed Calogero-Sutherland model in the context of the fractional quantum Hall effect (FQHE). A key aspect for this work is the introduction of the dual anyon field operators, which obey a natural generalization of the canonical anti-commutation relation.