Available at: https://digitalcommons.calpoly.edu/theses/2844
Date of Award
6-2024
Degree Name
MS in Mathematics
Department/Program
Mathematics
College
College of Science and Mathematics
Advisor
Sean Gasiorek
Advisor Department
Mathematics
Advisor College
College of Science and Mathematics
Abstract
Representation theory, which encodes the elements of a group as linear operators on a vector space, has far-reaching implications in physics. Fundamental results in quantum physics emerge directly from the representations describing physical symmetries. We first examine the connections between specific representations and the principles of quantum mechanics. Then, we shift our focus to the braid group, which describes the algebraic structure of braids. We apply representations of the braid group to physical systems in order to investigate quasiparticles known as anyons. Finally, we obtain governing equations of anyonic systems to highlight the differences between braiding statistics and conventional Bose-Einstein/Fermi-Dirac statistics.
Included in
Algebra Commons, Other Mathematics Commons, Other Physical Sciences and Mathematics Commons, Other Physics Commons, Quantum Physics Commons