Now showing items 1-3 of 3

• #### On Enumerative Structures in Quantum Field Theory ﻿

(University of Waterloo, 2020-07-13)
This thesis addresses a number of enumerative problems that arise in the context of quantum field theory and in the process of renormalization. In particular, the enumeration of rooted connected chord diagrams is further ...
• #### On Hopf Ore Extensions and Zariski Cancellation Problems ﻿

(University of Waterloo, 2020-04-29)
In this thesis, we investigate Ore extensions of Hopf algebras and the Zariski Cancellation problem for noncommutative rings. In particular, we improve upon the existing conditions for when $T=R[x; \sigma, \delta]$ is a ...
• #### Sequences of Trees and Higher-Order Renormalization Group Equations ﻿

(University of Waterloo, 2019-08-27)
In 1998, Connes and Kreimer introduced a combinatorial Hopf algebra HCK on the vector space of forests of rooted trees that precisely explains the phenomenon of renormalization in quantum field theory. This Hopf algebra ...

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