Dissertations, Theses, and Capstone Projects
Date of Degree
9-2016
Document Type
Dissertation
Degree Name
Ph.D.
Program
Physics
Advisor
V. Parameswaran Nair
Advisor
Scott O. Wilson
Committee Members
Alexios Polychronakos
Thomas Tradler
S. G. Rajeev
Subject Categories
Algebra | Elementary Particles and Fields and String Theory | Geometry and Topology | Quantum Physics
Keywords
principal bundle, holonomy, gauge theory, entropy, states on C*-algebras, GNS construction
Abstract
2-categories provide a useful transition point between ordinary category theory and infinity-category theory where one can perform concrete computations for applications in physics and at the same time provide rigorous formalism for mathematical structures appearing in physics. We survey three such broad instances. First, we describe two-dimensional algebra as a means of constructing non-abelian parallel transport along surfaces which can be used to describe strings charged under non-abelian gauge groups in string theory. Second, we formalize the notion of convex and cone categories, provide a preliminary categorical definition of entropy, and exhibit several examples. Thirdly, we provide a universal description of the Gelfand-Naimark-Segal construction as a canonical procedure from states on C*-algebras to representations of C*-algebras equipped with pure state.
Recommended Citation
Parzygnat, Arthur, "Some 2-Categorical Aspects in Physics" (2016). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/1475
Included in
Algebra Commons, Elementary Particles and Fields and String Theory Commons, Geometry and Topology Commons, Quantum Physics Commons