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Dissertations / Theses on the topic 'Lattice theory'

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Published: 4 June 2021

Last updated: 30 July 2024

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1

Race, David M. (David Michael). "Consistency in Lattices." Thesis, North Texas State University, 1986. https://digital.library.unt.edu/ark:/67531/metadc331688/.

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Let L be a lattice. For x ∈ L, we say x is a consistent join-irreducible if x V y is a join-irreducible of the lattice [y,1] for all y in L. We say L is consistent if every join-irreducible of L is consistent. In this dissertation, we study the notion of consistent elements in semimodular lattices.

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2

Radu, Ion. "Stone's representation theorem." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3087.

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The thesis analyzes some aspects of the theory of distributive lattices, particularly two representation theorems: Birkhoff's representation theorem for finite distributive lattices and Stone's representation theorem for infinite distributive lattices.

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3

Endres, Michael G. "Topics in lattice field theory /." Thesis, Connect to this title online; UW restricted, 2007. http://hdl.handle.net/1773/9713.

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4

Bowman, K. "A lattice theory for algebras." Thesis, Lancaster University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.234611.

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5

Michels, Amanda Therese. "Aspects of lattice gauge theory." Thesis, University of Oxford, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.297217.

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6

Buckle, John Francis. "Computational aspects of lattice theory." Thesis, University of Warwick, 1989. http://wrap.warwick.ac.uk/106446/.

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The use of computers to produce a user-friendly safe environment is an important area of research in computer science. This dissertation investigates how computers can be used to create an interactive environment for lattice theory. The dissertation is divided into three parts. Chapters two and three discuss mathematical aspects of lattice theory, chapter four describes methods of representing and displaying distributive lattices and chapters five, six and seven describe a definitive based environment for lattice theory. Chapter two investigates lattice congruences and pre-orders and demonstrates that any lattice congruence or pre-order can be determined by sets of join-irreducibles. By this correspondence it is shown that lattice operations in a quotient lattice can be calculated by set operations on the join-irreducibles that determine the congruence. This alternative characterisation is used in chapter three to obtain closed forms for all replacements of the form "h can replace g when computing an element f", and hence extends the results of Beynon and Dunne into general lattices. Chapter four investigates methods of representing and displaying distributive lattices. Techniques for generating Hasse diagrams of distributive lattices are discussed and two methods for performing calculations on free distributive lattices and their respective advantages are given. Chapters five and six compare procedural and functional based notations with computer environments based on definitive notations for creating an interactive environment for studying set theory. Chapter seven introduces a definitive based language called Pecan for creating an interactive environment for lattice theory. The results of chapters two and three are applied so that quotients, congruences and homomorphic images of lattices can be calculated efficiently.

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7

Craig, Andrew Philip Knott. "Lattice-valued uniform convergence spaces the case of enriched lattices." Thesis, Rhodes University, 2008. http://hdl.handle.net/10962/d1005225.

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Using a pseudo-bisymmetric enriched cl-premonoid as the underlying lattice, we examine different categories of lattice-valued spaces. Lattice-valued topological spaces, uniform spaces and limit spaces are described, and we produce a new definition of stratified lattice-valued uniform convergence spaces in this generalised lattice context. We show that the category of stratified L-uniform convergence spaces is topological, and that the forgetful functor preserves initial constructions for the underlying stratified L-limit space. For the case of L a complete Heyting algebra, it is shown that the category of stratified L-uniform convergence spaces is cartesian closed.

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8

Pugh, David John Rhydwyn. "Topological structures in lattice gauge theory." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.279896.

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9

Schaich, David. "Strong dynamics and lattice gauge theory." Thesis, Boston University, 2012. https://hdl.handle.net/2144/32057.

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Thesis (Ph.D.)--Boston University
In this dissertation I use lattice gauge theory to study models of electroweak symmetry breaking that involve new strong dynamics. Electroweak symmetry breaking (EWSB) is the process by which elementary particles acquire mass. First proposed in the 1960s, this process has been clearly established by experiments, and can now be considered a law of nature. However, the physics underlying EWSB is still unknown, and understanding it remains a central challenge in particle physics today. A natural possibility is that EWSB is driven by the dynamics of some new, strongly-interacting force. Strong interactions invalidate the standard analytical approach of perturbation theory, making these models difficult to study. Lattice gauge theory is the premier method for obtaining quantitatively-reliable, nonperturbative predictions from strongly-interacting theories. In this approach, we replace spacetime by a regular, finite grid of discrete sites connected by links. The fields and interactions described by the theory are likewise discretized, and defined on the lattice so that we recover the original theory in continuous spacetime on an infinitely large lattice with sites infinitesimally close together. The finite number of degrees of freedom in the discretized system lets us simulate the lattice theory using high-performance computing. Lattice gauge theory has long been applied to quantum chromodynamics, the theory of strong nuclear interactions. Using lattice gauge theory to study dynamical EWSB, as I do in this dissertation, is a new and exciting application of these methods. Of particular interest is non-perturbative lattice calculation of the electroweak S parameter. Experimentally S ~ -0.15(10), which tightly constrains dynamical EWSB. On the lattice, I extract S from the momentum-dependence of vector and axial-vector current correlators. I created and applied computer programs to calculate these correlators and analyze them to determine S. I also calculated the masses and other properties of the new particles predicted by these theories. I find S > 0.1 in the specific theories I study. Although this result still disagrees with experiment, it is much closer to the experimental value than is the conventional wisdom S > 0.3. These results encourage further lattice studies to search for experimentally viable strongly-interacting theories of EWSB.

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10

Schenk, Stefan. "Density functional theory on a lattice." kostenfrei, 2009. http://d-nb.info/998385956/34.

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11

Bär, Oliver. "Chiral perturbation theory for lattice QCD." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2011. http://dx.doi.org/10.18452/13976.

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Eine zusammenfassende Übersicht über die Formulierung der chiralen Störungstheorie (ChPT) für die Gitter Quantenchromodynamik (QCD) ist gegeben. Wir beginnen mit kurzen Zusammenfassungen der chiralen Störungstheorie für die Kontinuum-QCD sowie Symanziks effektiver Theorie für die Gitter-QCD. Anschließend wird die Formulierung der ChPT für die Gitter-QCD behandelt. Nach einem weiteren Kapitel über partial quenching und Theorien mit gemischten Wirkungen werden konkrete Anwendungen diskutiert: Wilson ChPT, staggered ChPT sowie Wilson ChPT mit einem chiral verdrehten Massenterm. Die folgenden Kapitel behandeln das Epsilonregime mit Wilsonfermionen sowie ausgewählte Resultate für ChPT mit gemischten Wirkungen. Den Abschluß bildet die Formulierung der chiralen Störungstheorie für schwere Vektormesonen mit Wilsonfermionen.
The formulation of chiral perturbation theory (ChPT) for lattice Quantum Chromodynamics (QCD) is reviewed. We start with brief summaries of ChPT for continuum QCD as well as the Symanzik effective theory for lattice QCD. We then review the formulation of ChPT for lattice QCD. After an additional chapter on partial quenching and mixed action theories various concrete applications are discussed: Wilson ChPT, staggered ChPT and Wilson ChPT with a twisted mass term. The remaining chapters deal with the epsilon regime with Wilson fermions and selected results in mixed action ChPT. Finally, the formulation of heavy vector meson ChPT with Wilson fermions is discussed.

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12

Du, Daping. "Fisher's zeros in lattice gauge theory." Diss., University of Iowa, 2011. https://ir.uiowa.edu/etd/1217.

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In this thesis, we study the Fisher's zeros in lattice gauge theory. The analysis of singularities in the complex coupling plane is an important tool to understand the critical phenomena of statistical models. The Fisher's zero structure characterizes the scaling properties of the underlying models and has a strong influence on the complex renormalization group transformation flows in the region away from both the strong and weak coupling regimes. By reconstructing the density of states, we try to develop a systematical method to investigate these singularities and we apply the method to SU(2) and U(1) lattice gauge models with a Wilson action in the fundamental representation. We first take the perturbative approach. By using the saddle point approximation, we construct the series expansions of the density of states in both of the strong and weak regimes from the strong and weak coupling expansions of the free energy density. We analyze the SU(2) and U(1) models. The expansions in the strong and weak regimes for the two models indicate both possess finite radii of convergence, suggesting the existence of complex singularities. We then perform the numerical calculations. We use Monte Carlo simulations to construct the numerical density of states of the SU(2) and U(1) models. We also discuss the convergence of the Ferrenberg-Swendsen's method which we use for the SU(2) model and propose a practical method to find the initial values that improve the convergence of the iterations. The strong and weak series expansions are in good agreement with the numerical results in their respective limits. The numerical calculations also enable the discussion of the finite volume effects which are important to the weak expansion. We calculate the Fisher's zeros of the SU(2) and U(1) models at various volumes using the numerical entropy density functions. We compare different methods of locating the zeros. By the assumption of validity of the saddle point approximation, we find that the roots of the second derivative of the entropy density function have an interesting relation with the actual zeros and may possibly reveal the scaling property of the zeros. Using the analytic approximation of the numerical density of states, we are able to locate the Fisher's zeros of the SU(2) and U(1) models. The zeros of the SU(2) stabilize at a distance from the real axis, which is compatible with the scenario that a crossover instead of a phase transition is expected in the infinite volume limit. In contrast, with the precise determination of the locations of Fisher's zeros for the U(1) model at smaller lattice sizes L=4, 6 and 8, we show that the imaginary parts of the zeros decrease with a power law of L-3.07 and pinch the real axis at β= 1.01134, which agrees with results using other methods. Preliminary results at larger volumes indicate a first-order transition in the infinite volume limit.

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13

Gragg, Karen E. (Karen Elizabeth). "Dually Semimodular Consistent Lattices." Thesis, North Texas State University, 1988. https://digital.library.unt.edu/ark:/67531/metadc330641/.

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A lattice L is said to be dually semimodular if for all elements a and b in L, a ∨ b covers b implies that a covers a ∧ b. L is consistent if for every join-irreducible j and every element x in L, the element x ∨ j is a join-irreducible in the upper interval [x,l]. In this paper, finite dually semimodular consistent lattices are investigated. Examples of these lattices are the lattices of subnormal subgroups of a finite group. In 1954, R. P. Dilworth proved that in a finite modular lattice, the number of elements covering exactly k elements is equal to the number of elements covered by exactly k elements. Here, it is established that if a finite dually semimodular consistent lattice has the same number of join-irreducibles as meet-irreducibles, then it is modular. Hence, a converse of Dilworth's theorem, in the case when k equals 1, is obtained for finite dually semimodular consistent lattices. Several combinatorial results are shown for finite consistent lattices similar to those already established for finite geometric lattices. The reach of an element x in a lattice L is the difference between the rank of x*, the join of x and all the elements covering x, and the rank of x; the maximum reach of all elements in L is the reach of L. Sharp lower bounds for the total number of elements and the number of elements of a given reach in a semimodular consistent lattice given the rank, the reach, and the number of join-irreducibles are found. Extremal lattices attaining these bounds are described. Similar results are then obtained for finite dually semimodular consistent lattices.

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14

Weston, Robert Andrew. "Lattice field theory and statistical-mechanical models." Thesis, University of Cambridge, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.315971.

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15

West, Stephen T. "Z(3) interfaces in lattice gauge theory." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.320664.

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16

Watson, Nicholas Jay. "Coupled cluster methods in lattice gauge theory." Thesis, University of Oxford, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305424.

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17

Tickle, Graham Alexander. "Glueballs in SU(2) lattice gauge theory." Thesis, University of Liverpool, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.316546.

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18

Scott, C. J. "Nucleon wave function from lattice gauge theory." Thesis, University of Southampton, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.379111.

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19

Kieu, T. D. "Theory and applications of lattice fermionic regularisations." Thesis, University of Edinburgh, 1988. http://hdl.handle.net/1842/10991.

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20

McNeile, Craig. "Lattice gauge theory calculations of hadron phenomenology." Thesis, University of Edinburgh, 1992. http://hdl.handle.net/1842/15359.

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In this thesis I study Quantum Chromodynamics on the lattice. A central theme will be the concept of improvement; this is choosing the lattice Lagrangian to minimise the effects of the lattice spacing on the results from numerical simulation. The first chapter reviews lattice gauge theory and introduces the idea of improvement. The techniques used in numerical simulations are briefly described. The second chapter will discuss whether an improved fermion lattice action called the clover action, obeys the reflection positivity condition. This is related to the existence of a transfer matrix. In the third chapter I will study the clover action in the strong coupling limit. Results for the pion and rho masses will be reported. A calculation of the O(a) lattice artifact correction to the gluon vacuum polarisation diagram for the clover action is described in chapter 4. The penultimate chapter contains results from various numerical simulations of lattice QCD using the clover action. The masses of some P-wave mesons will be reported, and used in a calculation of the QCD coupling. Results from a simulation of particles at finite momentum will be discussed.

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21

Stephanov, Mikhail Alexeevich. "Scalar-fermion theories on the lattice." Thesis, University of Oxford, 1994. http://ora.ox.ac.uk/objects/uuid:555a30de-2df9-4d39-b2dc-1974398911f7.

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We study scalar-fermion models with Yukawa interaction on a space-time lat- tice. Such models can describe the Higgs sector of the Standard Model in the case when the Higgs particle is very heavy (few hundred GeV) and there are very heavy fermions whose masses are due to their Yukawa interactions with the Higgs field. We study a realistic model with four component scalar field as well as simplified models with one and two component scalar fields. We use a mean field approximation to calculate equations for critical lines in the large d (dimension of space-time) limit. These lines are in very good agreement with available Monte Carlo data for the models at d = 4. We calculate fermion correlation functions in the mean field and large d approximations to study properties of different phases in the lattice models. We find two distinct phases with vanishing expectation values of the scalar field. One (at small Yukawa coupling Y) contains massless fermions, while in the other (at large F) the fermions have masses larger than the scale given by the inverse lattice spacing. We find that in the latter phase fermions can form bosonic bound states. These states show up as poles in a four-fermion correlator. We discuss pos- sible continuum limits in the lattice scalar-fermion models. In particular, we show that a theory defined near the critical line separating the disordered phase from the phase with antiferromagnetic order is not unitary.

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22

Roweth, Duncan. "Parallel algorithms for lattice QCD." Thesis, University of Edinburgh, 1987. http://hdl.handle.net/1842/12886.

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23

Barresi, Andrea. "SO(3) Yang-Mills theory on the lattice." Doctoral thesis, [S.l.] : [s.n.], 2003. http://deposit.ddb.de/cgi-bin/dokserv?idn=968943675.

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24

Van, de Water Ruth S. "Applications of chiral perturbation theory to lattice QCD /." Thesis, Connect to this title online; UW restricted, 2005. http://hdl.handle.net/1773/9730.

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25

Bursa, Francis. "Phase transitions in SU(N) lattice gauge theory." Thesis, University of Oxford, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.437179.

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26

Hart, A. "Magnetic monopoles and confinement in lattice gauge theory." Thesis, University of Oxford, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.337718.

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27

Riddell, A. G. "Computer algorithms for Euclidean lattice gauge theory calculations." Thesis, University of Canterbury. Physics, 1988. http://hdl.handle.net/10092/8220.

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The computer algorithm devised by K. Decker [25] for the calculation of strong coupling expansions in Euclidean lattice gauge theory is reviewed. Various shortcomings of this algorithm are pointed out and an improved algorithm is developed. The new algorithm does away entirely with the need to store large amounts of information, and is designed in such a way that memory useage is essentially independant of the order to which the expansion is being calculated. A good deal of the redundancy and double handling present in the algorithm of ref. [25] is also eliminated. The algorithm has been used to generate a 14th order expansion for the energy of a glue ball with non-zero momentum in Z₂ lattice gauge theory in 2+1 dimensions. The resulting expression is analysed in order to study the restoration of Lorentz invariance as the theory approaches the continuum. A description is presented of the alterations required to extend the algorithm to calculations in 3+1 dimensions. An eighth order expansion of the z₂ mass gap in 3+1 dimensions has been calculated. The eighth order term differs from a previously published result.

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28

Böhm, Walter. "Lattice path counting and the theory of queues." Department of Statistics and Mathematics, WU Vienna University of Economics and Business, 2008. http://epub.wu.ac.at/1086/1/document.pdf.

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In this paper we will show how recent advances in the combinatorics of lattice paths can be applied to solve interesting and nontrivial problems in the theory of queues. The problems we discuss range from classical ones like M^a/M^b/1 systems to open tandem systems with and without global blocking and to queueing models that are related to random walks in a quarter plane like the Flatto-Hahn model or systems with preemptive priorities. (author´s abstract)
Series: Research Report Series / Department of Statistics and Mathematics

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29

Wagner, Alexander. "Theory and applications of the lattice Boltzmann method." Thesis, University of Oxford, 1997. http://ora.ox.ac.uk/objects/uuid:882b9026-22cd-4e77-95e5-aca62f93df11.

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30

Lamont, M. J. "Hamiltonian lattice gauge theory : A cluster expansion approach." Thesis, University of Liverpool, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382063.

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31

Hesse, Dirk. "Automated lattice perturbation theory in the Schrödinger functional." Doctoral thesis, Humboldt-Universität zu Berlin, Mathematisch-Naturwissenschaftliche Fakultät I, 2012. http://dx.doi.org/10.18452/16642.

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Der Autor hat das pastor-Softwarepaket für automatisierte Gitterstörungstheorie im Schrödingerfunktional entwickelt. Das pastor-Paket besteht aus zwei Bausteinen, die die Erzeugung von Vertexfunktionen und Feynmandiagrammen übernehmen. Ausgehend von recht generischen Formulierungen der Gitterwirkungen für Fermionen und Gluonen, die dem Vertexgenerator in symbolischer Form übergeben werden, erzeugt dieser Feynmanregeln zu beliebiger Ordnung in der nackten Kopplung. Dabei kann sowohl ein triviales als auch ein Abelsches Hintergrundfeld verwendet werden. Die vom zweiten Teil von pastor, einem Code-Generator, erzeugten Programme greifen auf den Vertexgenerator zu und berechnen alle Terme der perturbativen Entwicklung für eine Klasse von Schrödingerfunktional-Observablen bis zur Einschleifenordnung. Verbesserungsterme der Ordnung a werden dabei berücksichtigt. Wir werden die für die Funktionen der beiden Teile von pastor relevanten Algorithmen detailliert beschrieben und die Korrektheit unserer Implementierung mit einer Reihe von Vergleichen mit perturbativen und nichtperturbativen Daten belegen. Wir werden darauf die Nützlichkeit von pastor Anhand einiger Beispiele aus dem Abgleich von Heavy Quark Effective Theory mit Quantenchromodynamik demonstrieren. Wir haben unter Anderem eine Einschleifenrechnung zweier Kandidaten für Observablen, die aller Voraussicht nach in Zukunft für den Abgleich verwendet werden, zügig und mit geringem Aufwand durchgeführt. Dies zeigt die Stärken eines Softwarepakets für automatisierte Störungsrechnungen. Unsere Resultate werden als nützliche Richtschnur für zukünftige nichtperturbative Berechnungen dienen.
The author developed the pastor software package for automated lattice perturbation theory calculations in the Schrödinger functional scheme. The pastor code consists of two building blocks, dealing with the generation of Feynman rules and Feynman diagrams respectively. Accepting a rather generic class of lattice gauge and fermion actions, passed to the code in a symbolic form as input, a low level part of pastor will generate Feynman rules to an arbitrary order in the bare coupling with a trivial or an Abelian background field. The second, high level part of pastor is a code generator whose output relies on the vertex generator. It writes programs that evaluate Feynman diagrams for a class of Schrödinger functional observables up to one loop order automatically, the relevant O(a) improvement terms are taken into account. We will describe the algorithms used for implementation of both parts of the code in detail, and provide cross checks with perturbative and non-perturbative data to demonstrate the correctness of our code. We demonstrate the usefulness of the pastor package through various applications taken from the matching process of heavy quark effective theory with quantum chromodynamics. We have e.g. completed a one loop analysis for new candidates for matching observables timely and with rather small effort, highlighting two advantages of an automated software setup. The results that were obtained so far will be useful as a guideline for further non-perturbative studies.

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32

Luo, Li-Shi. "Lattice-gas automata and lattice Boltzmann equations for two-dimensional hydrodynamics." Diss., Georgia Institute of Technology, 1993. http://hdl.handle.net/1853/30259.

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33

Heeney, Xiang Xia Huang. "Small lattices." Thesis, University of Hawaii at Manoa, 2000. http://hdl.handle.net/10125/25936.

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This dissertation introduces triple gluing lattices and proves that a triple gluing lattice is small if the key subcomponents are small. Then attention is turned to triple gluing irreducible small lattices. The triple gluing irreducible [Special characters omitted.] lattices are introduced. The conditions which insure [Special characters omitted.] small are discovered. This dissertation also give some triple gluing irreducible small lattices by gluing [Special characters omitted.] 's. Finally, K-structured lattices are introduced. We prove that a K-structured lattice L is triple gluing irreducible if and only if [Special characters omitted.] . We prove that no 4-element antichain lies in u 1 /v1 of a K-structured small lattice. We also prove that some special lattices with 3-element antichains can not lie in u1 /v1 of a K-structured small lattice.
viii, 87 leaves, bound : ill. ; 29 cm.
Thesis (Ph. D.)--University of Hawaii at Manoa, 2000.

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34

McCallum, Paul. "Upsilon spectroscopy using lattice QCD." Thesis, University of Glasgow, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.363170.

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35

Coddington, P. D. "Deconfinement transitions in lattice gauge theories]." Thesis, University of Southampton, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381129.

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36

Smith, Joseph Patrick. "Groups whose normalizers form a lattice." Diss., Online access via UMI:, 2006.

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37

Bystrik, Anna. "On Delocalization Effects in Multidimensional Lattices." Thesis, University of North Texas, 1998. https://digital.library.unt.edu/ark:/67531/metadc278868/.

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A cubic lattice with random parameters is reduced to a linear chain by the means of the projection technique. The continued fraction expansion (c.f.e.) approach is herein applied to the density of states. Coefficients of the c.f.e. are obtained numerically by the recursion procedure. Properties of the non-stationary second moments (correlations and dispersions) of their distribution are studied in a connection with the other evidences of transport in a one-dimensional Mori chain. The second moments and the spectral density are computed for the various degrees of disorder in the prototype lattice. The possible directions of the further development are outlined. The physical problem that is addressed in the dissertation is the possibility of the existence of a non-Anderson disorder of a specific type. More precisely, this type of a disorder in the one-dimensional case would result in a positive localization threshold. A specific type of such non-Anderson disorder was obtained by adopting a transformation procedure which assigns to the matrix expressing the physics of the multidimensional crystal a tridiagonal Hamiltonian. This Hamiltonian is then assigned to an equivalent one-dimensional tight-binding model. One of the benefits of this approach is that we are guaranteed to obtain a linear crystal with a positive localization threshold. The reason for this is the existence of a threshold in a prototype sample. The resulting linear model is found to be characterized by a correlated and a nonstationary disorder. The existence of such special disorder is associated with the absence of Anderson localization in specially constructed one-dimensional lattices, when the noise intensity is below the non-zero critical value. This work is an important step towards isolating the general properties of a non-Anderson noise. This gives a basis for understanding of the insulator to metal transition in a linear crystal with a subcritical noise.

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38

Jipsen, Peter. "Varieties of lattices." Master's thesis, University of Cape Town, 1988. http://hdl.handle.net/11427/15851.

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Bibliography: pages 140-145.
An interesting problem in universal algebra is the connection between the internal structure of an algebra and the identities which it satisfies. The study of varieties of algebras provides some insight into this problem. Here we are concerned mainly with lattice varieties, about which a wealth of information has been obtained in the last twenty years. We begin with some preliminary results from universal algebra and lattice theory. The next chapter presents some properties of the lattice of all lattice sub-varieties. Here we also discuss the important notion of a splitting pair of varieties and give several characterisations of the associated splitting lattice. The more detailed study of lattice varieties splits naturally into the study of modular lattice varieties and non-modular lattice varieties, dealt with in the second and third chapter respectively. Among the results discussed there are Freese's theorem that the variety of all modular lattices is not generated by its finite members, and several results concerning the question which varieties cover a given variety. The fourth chapter contains a proof of Baker's finite basis theorem and some results about the join of finitely based lattice varieties. Included in the last chapter is a characterisation of the amalgamation classes of certain congruence distributive varieties and the result that there are only three lattice varieties which have the amalgamation property.

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39

Meskine, Hakim. "Theory of lattice effects on magnetic interactions in solids." Diss., Columbia, Mo. : University of Missouri-Columbia, 2005. http://hdl.handle.net/10355/4121.

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Thesis (Ph. D.)--University of Missouri-Columbia, 2005.
The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file viewed on (November 13, 2006) Vita. Includes bibliographical references.

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40

Söldner, Wolfgang. "Chiral fermions in lattice QCD and random matrix theory." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972268839.

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41

Monahan, Christopher John. "The application of automated perturbation theory to lattice QCD." Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/241041.

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Predictions of heavy quark parameters are an integral component of precision tests of the Standard Model of particle physics. Experimental measurements of electroweak processes involving heavy hadrons provide stringent tests of Cabibbo-Kobayashi-Maskawa (CKM) matrix unitarity and serve as a probe of new physics. Hadronic matrix elements parameterise the strong dynamics of these interactions and these matrix elements must be calculated nonperturbatively. Lattice quantum chromodynamics (QCD) provides the framework for nonperturbative calculations of QCD processes. Current lattices are too coarse to directly simulate b quarks. Therefore an effective theory, nonrelativistic QCD (NRQCD), is used to discretise the heavy quarks. High precision simulations are required so systematic uncertainties are removed by improving the NRQCD action. Precise simulations also require improved sea quark actions, such as the highly-improved staggered quark (HISQ) action. The renormalisation parameters of these actions cannot be feasibly determined by hand and thus automated procedures have been developed. In this dissertation I apply automated lattice pertubartion theory to a number of heavy quark calculations. I first review the fundamentals of lattice QCD and the construction of lattice NRQCD. I then motivate and discuss lattice perturbation theory in detail, focussing on the tools and techniques that I use in this dissertation. I calculate the two-loop tadpole improvement factors for improved gluons with improved light quarks. I then compute the renormalisation parameters of NRQCD. I use a mix of analytic and numerical methods to extract the one-loop radiative corrections to the higher order kinetic operators in the NRQCD action. I then employ a fully automated procedure to calculate the heavy quark energy shift at two-loops. I use this result to extract a new prediction of the mass of the b quark from lattice NRQCD simulationsby the HPQCD collaboration. I also review the calculation of the radiative corrections to the chromo-magnetic operator in the NRQCD action. This computation is the first outcome of our implementation of background field gauge for automated lattice perturbation theory. Finally, I calculate the heavy-light currents for highly-improved NRQCD heavy quarks with massless HISQ light quarks and discuss the application of these results to nonperturbative studies by the HPQCD collaboration.

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42

Copeland, Timothy John. "Monoplies and confinement in U(1) lattice gauge theory." Thesis, University of Oxford, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.305986.

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Bougenaya, Yamina. "Fermion models on the lattice and in field theory." Thesis, Durham University, 1985. http://etheses.dur.ac.uk/7080/.

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The first part deals with lattice approach to field theories. The fermion doubling problems are described. This doubling can be removed if a dual lattice is introduced, as first pointed out by Stacey. His method is developed and in the process a formalism for the construction of a covariant difference lattice operator and thus of a gauge invariant action, is exhibited. It is shown how this formalism relates to the work of Wilson. Problems of gauge invariance can be traced back to the absence of the Leibnitz rule on the lattice. To circumvent this failure the usual notion of the product is replaced by a convolution. The solutions display a complementarity : the more localised the product the more extended is the approximation to the derivative and vice-versa. It is found that the form of the difference operator in the continuous limit dictates the formulation of the full two-dimensional supersymmetric algebra. The construction of the fields necessary to form the Wess-Zumino model follows from the requirement of anticommutativity of the supersymmetric charges. In the second part, the Skyrme model is reviewed and Bogomolnyi conditions are defined and discussed. It appears that while the Skyrme model has many satisfactory features, it fails to describe the interactions between nucleons correctly. These problems are brought out and the available solutions reviewed.

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44

Preece, Timothy Edward. "Cluster expansion approach to non-Abelian lattice gauge theory." Thesis, University of Liverpool, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328162.

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45

Husung, Nikolai. "Logarithmic corrections in Symanzik’s effective theory of lattice QCD." Doctoral thesis, Humboldt-Universität zu Berlin, 2021. http://dx.doi.org/10.18452/22944.

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Einer der finalen Schritte in Simulationen von Gitter Quantenchromodynamik (QCD) oder Gittereichtheorie ist die Kontinuumsextrapolation, um die eigentliche Kontinuumsphysik zu extrahieren. Diese Extrapolation beruht stark auf Annahmen über die asymptotische Abhängigkeit vom Gitterabstand, was zu systematischen Unsicherheiten des Kontinuumslimes führt. In klassischen Feldtheorien ist die asymptotische Form schlicht eine Potenzreihe im Gitterabstand, wobei die führende Potenz von der gewählten Diskretisierung auf dem Gitter abhängt. Die Quantenkorrekturen in Gitter QCD und Gittereichtheorie brechen dieses Verhalten. Für asymptotisch freie Theorien wie Gitter QCD werden die ganzzahligen Potenzen im Gitterabstand mit einer Potenz der laufenden Kopplung multipliziert. Die führenden Potenzen in der Kopplung lassen sich wiederum aus den anomalen Dimensionen von höher-dimensionalen Operatoren bestimmen, die eine Basis für eine Symanzik Effektiven Feldtheorie bilden. Im Rahmen dieser Arbeit werden die führenden Potenzen in der Kopplung für die Wilson oder Ginsparg-Wilson (GW) Wirkung bestimmt, die für spektrale Größen wie Hadronmassen beitragen. Die untere Schranke des Spektrums dieser Potenzen liegt nahe null für Gitter QCD mit Wilson oder GW Quarks, weshalb keine Probleme durch eine verschlechterte Konvergenz zum Kontinuumslimes zu erwarten sind. Allerdings ist das Spektrum der führenden Potenzen sehr dicht. Dadurch lässt sich der Operator der minimalen Basis mit dominierendem Beitrag zu den Gitterartefakten schlecht bestimmen und ein kompliziertes Zusammenspiel der verschiedenen Beiträge zu den Gitterartefakten ist möglich. Nun, da die führenden Korrekturen der Gitterwirkungen mit Wilson und GW Quarks zur klassischen Potenz im Gitterabstand bekannt sind, sollten diese für die Kontinuumsextrapolation genutzt werden, sowohl für den Ansatz der Extrapolationsfunktion als auch als Orientierungshilfe, um die inhärente systematische Unsicherheit des Kontinuumslimes abzuschätzen.
One of the final steps in simulations of lattice Quantum Chromodynamics (QCD) or lattice pure gauge theory is the continuum extrapolation to extract the actual continuum physics. This extrapolation relies heavily on assumptions regarding the asymptotic dependence on the lattice spacing, which introduces an inherent systematic uncertainty to the continuum limit. In classical field theories the asymptotic form is a power series in the lattice spacing, where the leading power depends on the chosen lattice discretisation. The quantum nature of lattice QCD and lattice pure gauge theory spoils this behaviour. For asymptotically free theories like lattice QCD the integer powers in the lattice spacing are multiplied by an additional power in the running coupling. The leading powers in the coupling can be determined from the anomalous dimensions of higher dimensional operators, which form a minimal basis of a Symanzik Effective theory. The scope of this thesis is to compute the leading powers in the coupling for the Wilson or Ginsparg-Wilson (GW) action relevant for spectral quantities like hadron masses. The lower bound of these powers is close to zero for lattice QCD with Wilson or GW quarks such that no problems from a reduced convergence towards the continuum limit are to be expected. However the spectrum of leading powers is very dense. The operator of the minimal basis with dominant contributions to the lattice artifacts is thus hard to determine and complicated interplay of the contributions from the various operators is possible. Now the leading corrections from lattice actions with Wilson or GW quarks to the classical power in the lattice spacing are known and should be used when performing the continuum extrapolation both through explicit use in the fit ansatz and as an orientation to estimate the systematic uncertainty inherent to the continuum limit.

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Kusterer, Daniel-Jens. "Quark properties, topology and confinement from Lattice Gauge Theory." [S.l. : s.n.], 2004. http://www.bsz-bw.de/cgi-bin/xvms.cgi?SWB11514075.

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47

Schroeder, Christopher Robert. "Beyond the scalar Higgs, in lattice quantum field theory." Diss., [La Jolla] : University of California, San Diego, 2009. http://wwwlib.umi.com/cr/ucsd/fullcit?p3386720.

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Thesis (Ph. D.)--University of California, San Diego, 2009.
Title from first page of PDF file (viewed January 19, 2010). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 87-93).

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48

Arndt, Daniel. "Chiral perturbation theory on the lattice and its applications /." Thesis, Connect to this title online; UW restricted, 2004. http://hdl.handle.net/1773/9693.

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Wysong, Kimberly Ann. "Minimal embeddings of knots in the cubic lattice /." Abstract Full Text (PDF), 2008. http://eprints.ccsu.edu/archive/00000535/02/1984FT.pdf.

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Thesis (M.A.) -- Central Connecticut State University, 2008.
Thesis advisor: Nelson Castaneda. "... in partial fulfillment of the requirements for the degree of Master of Arts in Mathematical Sciences." Includes bibliographical references (leaves 98-99). Also available via the World Wide Web.

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Marcantonio, Laurence Mark. "Unquenched lattice upsilon spectroscopy." Thesis, University of Glasgow, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.341965.

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