Year: 2011
Type: dissertation
Abstract: In this thesis I present a mathematical tool for understanding the spin networks that \narise from the study of the loop states of quantum gravity. The spin networks that arise \nin quantum gravity possess more information than the original spin networks of Penrose: \nthey are embedded within a manifold and thus possess topological information. There \nare limited tools available for the study of this information. To remedy this I introduce \na slightly modi ed mathematical object - Braided Ribbon Networks - and demonstrate \nthat they can be related to spin networks in a consistent manner which preserves the \ndi eomorphism invariant character of the loop states of quantum gravity. \n \nGiven a consistent de nition of Braided Ribbon Networks I then relate them back to \nprevious trinion based versions of Braided Ribbon Networks. Next, I introduce a consistent evolution for these networks based upon the duality of these networks to simplicial complexes. From here I demonstrate that there exists an invariant of this evolution and smooth deformations of the networks, which captures some of the topological information of the networks. \n \nThe principle result of this program is presented next: that the invariants of the Braided Ribbon Networks can be transferred over to the original spin network states of loop quantum gravity. \n \nFrom here we represent other advances in the study of braided ribbon networks, accompanied \nby comments of their context given the consistent framework developed earlier \nincluding: the meaning of isolatable substructures, the particular structure of the capped three braids in trivalent braided ribbon networks and their application towards emergent particle physics, and the implications of the existence of microlocal topological structures in spin networks. \n \nLastly we describe the current state of research in braided ribbon networks, the implications of this study on quantum gravity as a whole and future directions of research in the area.
Source: UWSpace (University of Waterloo)
Author: Jonathan Hackett
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2590646497