Browsing Pure & Applied Mathematics by Title
Now showing items 167-186 of 390
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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 ... -
Highly excited and exotic meson spectrum from dynamical lattice QCD
(2009)Using a new quark-field construction algorithm and a large variational basis of operators, we extract a highly excited isovector meson spectrum on dynamical anisotropic lattices. We show how carefully constructed operators ... -
Holomorphic extension of smooth CR-mappings between real-analytic and real-algebraic CR-manifolds
(International Press, 2003)The classical Schwarz reflection principle states that a continuous map f between real-analytic curves M and M? in C that locally extends holomorphically to one side of M, extends also holomorphically to a neighborhood ... -
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 ... -
Hubbard-Shastry lattice models
(2012)We consider two lattice models for strongly correlated electrons which are exactly solvable in one dimension. Along with the Hubbard model and the $\mathfrak {su}(2|2)$ spin chain, these are the only parity-invariant models ... -
The Hydrodynamical Relevance of the Camassa?Holm and Degasperis?Procesi Equations
(Springer-Verlag, 2009-04-01)n recent years two nonlinear dispersive partial differential equations have attracted much attention due to their integrable structure. We prove that both equations arise in the modeling of the propagation of shallow water ... -
Icosahedral Skyrmions
(American Institute of Physics, 2003)In this article we aim to determine the baryon numbers at which the minimal energy Skyrmion has icosahedral symmetry. By comparing polyhedra which arise as minimal energy Skyrmions with the dual of polyhedra that minimize ... -
Improved stochastic estimation of quark propagation with Laplacian Heaviside smearing in lattice QCD
(2011)A new method of stochastically estimating the low-lying effects of quark propagation is proposed which allows accurate determinations of temporal correlations of single-hadron and multihadron operators in lattice QCD. The ... -
Improving Algorithms to Compute All Elements of the Lattice Quark Propagator
(Elsevier, 2005)We present a new exact algorithm for estimating all elements of the quark propagator. The advantage of the method is that the exact all-to-all propagator is reproduced in a large but finite number of inversions. The ... -
In search of a scaling scalar glueball
(Elsevier, 1999)Anisotropic lattices are an efficient means of studying the glueballs of QCD, however problems arise with simulations of the lightest, scalar state. The mass is strongly dependent on the lattice spacing, even when ... -
Indefinite theta series and generalised error functions
(2018)Theta series for lattices with indefinite signature ( n + ,n − ) arise in many areas of mathematics including representation theory and enumerative algebraic geometry. Their mod- ular properties are well understood ... -
Instanton vibrations of the 3-Skyrmion
(American Physical Society, 1999)The Atiyah-Drinfeld-Hitchin-Manin matrix corresponding to a tetrahedrally symmetric 3-instanton is calculated. Some small variations of the matrix correspond to vibrations of the instanton-generated 3-Skyrmion. These ... -
Integrable Hamiltonian for Classical Strings on AdS(5) x S**5
(Institute of Physics, 2005)We find the Hamiltonian for physical excitations of the classical bosonic string propagating in the AdS_5 x S^5 space-time. The Hamiltonian is obtained in a so-called uniform gauge which is related to the static gauge by ... -
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. ... -
Intersection cohomology of moduli spaces of sheaves on surfaces
(2018)We study intersection cohomology of moduli spaces of semist able vector bundles on a complex algebraic surface. Our main result relates inte rsection Poincar ́e polynomials of the moduli spaces to Donaldson-Thomas ... -
Inversion symmetric 3-monopoles and the Atiyah-Hitchin manifold
(IOP, 1996)We consider 3-monopoles symmetric under inversion symmetry. We show that the moduli space of these monopoles is an Atiyah?Hitchin submanifold of the 3-monopole moduli space. This allows what is known about 2-monopole ... -
Isoscalar meson spectroscopy from lattice QCD
(2011)We extract to high statistical precision an excited spectrum of single-particle isoscalar mesons using lattice QCD, including states of high spin and, for the first time, light exotic J(PC) isoscalars. The use of a novel ... -
Jordan systems, bounded symmetric domains and associated group orbits with holomorphic and CR extension theory
(Trinity College (Dublin, Ireland). School of Mathematics, 2006)The first chapter will deal with the one to one correspondence between the positive hermitian Jordan triple systems and the bounded symmetric domains. We start by defining the various Jordan systems. Then we continue by ...
