Now showing items 1-7 of 7

    • Aspects of Quantum Field Theory in Enumerative Graph Theory 

      Yusim, Samuel (University of Waterloo, 2022-10-24)
      While a quantum field theorist has many uses for mathematics of all kinds, the relationship between quantum field theory and mathematics is far too fluid in the world of modern research to be described as the simple provision ...
    • A Combinatorial Tale of Two Scattering Amplitudes: See Two Bijections 

      Hu, Simeng Simone (University of Waterloo, 2022-01-07)
      In this thesis, we take a journey through two different but not dissimilar stories with an underlying theme of combinatorics emerging from scattering amplitudes in quantum field theories. The first part tells the tale ...
    • Enumerative perspectives on chord diagrams 

      Nabergall, Lukas (University of Waterloo, 2022-10-07)
      The topic of this thesis is enumerating certain classes of chord diagrams, perfect matchings of the interval $\{1, 2, \ldots, 2n\}$. We consider hereditary classes of chord diagrams that are restricted to satisfy one of ...
    • Minimum Number of Triangles of K5 Descendants 

      Santoli, Steven (University of Waterloo, 2022-01-26)
      In the study of Quantum Field Theory and Feynman Periods, the operation of double triangle expansion plays an important role. This is largely due to double triangle expansions not affecting the maximum weight of the ...
    • On Enumerative Structures in Quantum Field Theory 

      Mahmoud, Ali (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 ...
    • Sequences of Trees and Higher-Order Renormalization Group Equations 

      Dugan, William (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 ...
    • Some Applications of Combinatorial Hopf Algebras to Integro-Differential Equations and Symmetric Function Identities 

      Olson-Harris, Nicholas (University of Waterloo, 2024-07-09)
      Hopf algebras built from combinatorial objects have found application both within combinatorics and, following the work of Connes and Kreimer, in quantum field theory. Despite the apparent gulf between these areas, the ...


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