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Now showing items 22-41 of 60

  • Decay widths from Euclidean quantum field theory a scalar model and applications to QCD 

    Nolan, Andrew (Trinity College (Dublin, Ireland). School of Mathematics, 2009)
    Lüscher provided a method by which the Euclidean correlation function, used in lattice field theories, can be used to evaluate the scattering phase shift, side-stepping the Maiani-Testa Theorem. This result is explored in ...
  • Discrete exterior calculus with applications to flows and spinors 

    De Beaucé, Vivien (Trinity College (Dublin, Ireland). School of Mathematics, 2005)
  • Efficient coding of sensory stimuli 

    Greene, Garrett (Trinity College (Dublin, Ireland). School of Mathematics, 2011)
    An important goal of mathematical neuroscience is to understand the coding principles governing the behaviour of sensory systems under stimulation. Here, we investigate the theory of efficient coding in nenral sensory ...
  • Elements of an operator calculus 

    Hughes, Arthur (Trinity College (Dublin, Ireland). School of Mathematics, 2001)
    The operational calculus developed by the Irish School of the Vienna Development Method (VDM) has a life of its own independent of its applications. This thesis is interested in the operational calculus that arose from the ...
  • Extending geometric discretisation 

    Sen, Samik (Trinity College (Dublin, Ireland). School of Mathematics, 2002)
    Geometric discretisation (GD) [1] is a novel approach capable of capturing topological properties, based on a correspondence between discrete objects and operations on a triangulation with continuum ones on a manifold. We ...
  • Form Factors, Integrability and the AdS/CFT Correspondence 

    GEROTTO, LORENZO (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 

    Britton, Stephen (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 ...
  • Higher Spin Theories in Twistor Space 

    HÄHNEL, PHILIPP (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 

    Tamaroff, Pedro Nicolas (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 

    Quinn, Eoin (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 

    Ryan, Paul (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 

    Smits, Olaf (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 

    Lawless, Eoin (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 

    Duffy, Ken (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 

    Cooney, Michael (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 

    Kitson, Derek (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 

    KORPAS, GEORGIOS (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 ...
  • Multidimensional second order generalised stochastic processes on locally compact Abelian groups 

    Keville, Bernard (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 

    Spiering, Anne (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 

    Foley, Justin (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 ...