Browsing Pure & Applied Mathematics (Theses and Dissertations) by Title
Now showing items 31-50 of 68
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Form Factors, Integrability and the AdS/CFT Correspondence
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2018)Form factors are matrix elements of local operators between scattering states, and are interesting off-shell objects in any QFT. In this thesis we will focus on the world-sheet theory describing strings in AdS5xS5, the ... -
Free Field Representation and Form Factors of the Chiral Gross-Neveu Model
(Trinity College (Dublin, Ireland). School of Mathematics, 2013)The process of using the free field representation to construct form factors of two dimensional integrable models is very promising. In this thesis, this procedure is analysed and adapted for application to the chiral ... -
Hadron Scattering Amplitudes from Lattice QCD
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2023)In this thesis we compute hadron scattering amplitudes within the framework of lattice quantum chromodynamics. Finite-volume spectra are computed using distillation and the variational method. These spectra constrain ... -
Heavy Hadron Spectroscopy from Lattice QCD
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2024)In this thesis, heavy hadron spectroscopy was studied through the formalism of lattice quantum chromodynamics. A summary of relevant theory is provided, followed by an overview of the current state-of-the-art spectroscopy ... -
Higher Spin Theories in Twistor Space
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2018)In this thesis we formulate an action principle for conformal higher spin theory on twistor space. For this theory, and for a unitary sub-sector that we identify, we construct an MHV amplitude expansion by considering ... -
Homotopical and effective methods for associative algebras
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2021)This thesis contains four main chapters based on four different papers. In the third chapter, we solve the problem of computing the minimal model of an arbitrary associative monomial algebra. Our methods are combinatorial ... -
Integrable lattice models for strongly correlated electrons
(Trinity College (Dublin, Ireland). School of Mathematics, 2013)This thesis is dedicated to the study of a new family of integrable lattice models for strongly correlated electrons, namely the Hubbard- Shastry models. The techniques of exactly solvable models, and in particular those ... -
Integrable systems, separation of variables and the Yang-Baxter equation
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2021)This thesis is based on the author’s publications during the course of his PhD studies and focuses on various aspects of the field of quantum integrable systems. The aim of this thesis is to develop the so-called separation ... -
Interferometry and non-equilibrium noise in the fractional quantum Hall effect
(Trinity College (Dublin, Ireland). School of Mathematics, 2014)We study theoretical aspects of fractional quantum Hall devices based on tunnelling point contacts. The fractional quantum Hall effect is the prime example of a (2 + 1) dimensional system with non-trivial topological order. ... -
Large scale parallel network simulation
(Trinity College (Dublin, Ireland). School of Mathematics, 2004)Simulation is one of the primary tools used in studying computer networks. However the difficulties of simulating a network grow with its size. With the hardware resources currently available it is not feasible to simulate ... -
Logarithmic asymptotics in Queueing Theory and Risk Theory
(Trinity College (Dublin, Ireland). School of Mathematics, 2000)This thesis addresses four distinct, but related, problems. All four involve large deviation theory. The first problem is to relate the logarithmic asymptotics of the single server queue length distribution to the long ... -
Methods for calculating option prices with early-exercise features
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)In this dissertation we deal with two distinct methods for pricing financial options with early-exercise features. First we use finite difference methods to calculate the prices, examining in particular two new schemes ... -
Methods of ascent and descent in multivariable spectral theory
(Trinity College (Dublin, Ireland). School of Mathematics, 2009)In this dissertation the theory of ascent and descent for a linear operator acting on a vector space is extended to arbitrary sets of operators and applied to the study of joint spectra for finite commuting systems of bounded ... -
Modern aspects of topological gauge theories - Polynomial invariants and mock modular forms
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)In this dissertation we present new results in the field of topologically twisted gauge theories evaluated on compact four-manifolds without boundary. We focus on the Donaldson-Witten theory, that is the N = 2 topologically ... -
Modularity in Supersymmetric Gauge Theory
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)In this thesis, we study the modularity and duality of Coulomb branches for a class of four-dimensional N=2 supersymmetric gauge theories. For pure N=2 super Yang-Mills theory with gauge group SU(2), the Coulomb branch can ... -
Multidimensional second order generalised stochastic processes on locally compact Abelian groups
(Trinity College (Dublin, Ireland). School of Mathematics, 2004)This thesis is concerned with the harmonic analysis of multidimensional generalised stochastic processes on locally compact Abelian groups. A multidimensional generalised stochastic process is a continuous linear operator ... -
Non-planar anomalous dimensions in super Yang-Mills theories
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2022)Conformal supersymmetric Yang--Mills theories play an important role in the gauge-gravity correspondence and, despite being highly non-physical, have been a driving force for many new approaches in more realistic theories ... -
Novel methods for heavy-quark physics from lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)The application of 3+1 anisotropic lattices to numerical simulations of hadrons containing heavy quarks is investigated. It is expected that using a fine temporal lattice spacing will suppress large mass-dependent errors ... -
On the Symanzik improvement of gradient flow observables
(Trinity College Dublin. School of Mathematics. Discipline of Pure & Applied Mathematics, 2019)The gradient flow provides a new class of renormalised observables which can be measured with high precision in lattice simulations. This is relevant for many interesting applications. However, such applications are made ... -
Peturbative study of the Chirally Rotated Schrödinger Functionality in Lattice QCD
(Trinity College (Dublin, Ireland). School of Mathematics, 2014)In this thesis we study the renormalisation and O(a) improvement of the Chirally Rotated Schrödinger Functional (xSF) in perturbation theory. The xSF was originally proposed in [1] as a way of rehabiliting the mechanism ...
