Download or read book Hamiltonian Lattice Field Theory written by Robert Zako and published by . This book was released on 1991 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lattice Quantum Field Theory Of The Dirac And Gauge Fields Selected Topics written by Belal Ehsan Baaquie and published by World Scientific. This book was released on 2020-07-30 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum Chromodynamics is the theory of strong interactions: a quantum field theory of colored gluons (Yang-Mills gauge fields) coupled to quarks (Dirac fermion fields). Lattice gauge theory is defined by discretizing spacetime into a four-dimensional lattice — and entails defining gauge fields and Dirac fermions on a lattice. The applications of lattice gauge theory are vast, from the study of high-energy theory and phenomenology to the numerical studies of quantum fields.Lattice Quantum Field Theory of the Dirac and Gauge Fields: Selected Topics examines the mathematical foundations of lattice gauge theory from first principles. It is indispensable for the study of Dirac and lattice gauge fields and lays the foundation for more advanced and specialized studies.
Download or read book Hamiltonian Lattice Field Theory written by and published by . This book was released on 1991 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt: I develop a variational method for systematic numerical computation of physical quantities -- bound state energies and scattering amplitudes -- in quantum field theory. An infinite-volume, continuum theory is approximated by a theory on a finite spatial lattice, which is amenable to numerical computation. I present an algorithm for computing approximate energy eigenvalues and eigenstates in the lattice theory and for bounding the resulting errors. I also show how to select basis states and choose variational parameters in order to minimize errors. The algorithm is based on the Rayleigh-Ritz principle and Kato's generalizations of Temple's formula. The algorithm could be adapted to systems such as atoms and molecules. I show how to compute Green's functions from energy eigenvalues and eigenstates in the lattice theory, and relate these to physical (renormalized) coupling constants, bound state energies and Green's functions. Thus one can compute approximate physical quantities in a lattice theory that approximates a quantum field theory with specified physical coupling constants. I discuss the errors in both approximations. In principle, the errors can be made arbitrarily small by increasing the size of the lattice, decreasing the lattice spacing and computing sufficiently long. Unfortunately, I do not understand the infinite-volume and continuum limits well enough to quantify errors due to the lattice approximation. Thus the method is currently incomplete. I apply the method to real scalar field theories using a Fock basis of free particle states. All needed quantities can be calculated efficiently with this basis. The generalization to more complicated theories is straightforward. I describe a computer implementation of the method and present numerical results for simple quantum mechanical systems.
Download or read book Introduction to Quantum Fields on a Lattice written by Jan Smit and published by Cambridge University Press. This book was released on 2002-09-19 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description
Download or read book Topics in Lattice Field Theory written by Mark Allen Srednicki and published by . This book was released on 1980 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lattice Gauge Theories written by Heinz J. Rothe and published by World Scientific. This book was released on 2005 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Wherever possible simple examples, which illustrate the main ideas, are provided before embarking on the actual discussion of the problem of interest - The book introduces the readers to problems of great current interest, like instantons, calorons, vortices, magnetic monopoles - QCD at finite temperature is discussed at great length, both in perturbation theory and in Monte Carlo simulations - The book contains many figures showing numerical results of pioneering work
Download or read book Long range Interactions in Lattice Field Theory written by Jeffrey Mark Rabin and published by . This book was released on 1981 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Phases of Quantum Chromodynamics written by John B. Kogut and published by Cambridge University Press. This book was released on 2003-12-24 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the physical phases of quantum chromodynamics (QCD) in ordinary environments and also in extreme environments of high temperatures and high baryon number. It introduces lattice gauge theory, covering fundamentals and important developments, and emphasises the application of QCD to the study of matter in extreme environments.
Download or read book Lattice Quantum Field Theory of the Dirac and Gauge Fields written by B. E. Baaquie and published by . This book was released on 2020 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Quantum Chromodynamics is the theory of strong interactions: a quantum field theory of colored gluons (Yang-Mills gauge fields) coupled to quarks (Dirac fermion fields). Lattice gauge theory is defined by discretizing spacetime into a four-dimensional lattice -- and entails defining gauge fields and Dirac fermions on a lattice. The applications of lattice gauge theory are vast, from the study of high-energy theory and phenomenology to the numerical studies of quantum fields. "Lattice Quantum Field Theory of the Dirac and Gauge Fields: Selected Topics" examines the mathematical foundations of lattice gauge theory from first principles. It is indispensable for the study of Dirac and lattice gauge fields and lays the foundation for more advanced and specialized studies"--Publisher's website.
Download or read book Quantum Fields on a Lattice written by Istvan Montvay and published by Cambridge University Press. This book was released on 1994 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a comprehensive and coherent account of the theory of quantum fields on a lattice.
Download or read book Lattice Gauge Theories An Introduction Third Edition written by Heinz J Rothe and published by World Scientific Publishing Company. This book was released on 2005-06-17 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a broad introduction to gauge field theories formulated on a space-time lattice, and in particular of QCD. It serves as a textbook for advanced graduate students, and also provides the reader with the necessary analytical and numerical techniques to carry out research on his own. Although the analytic calculations are sometimes quite demanding and go beyond an introduction, they are discussed in sufficient detail, so that the reader can fill in the missing steps. The book also introduces the reader to interesting problems which are currently under intensive investigation. Whenever possible, the main ideas are exemplified in simple models, before extending them to realistic theories. Special emphasis is placed on numerical results obtained from pioneering work. These are displayed in numerous figures.
Download or read book Lattice Quantum Chromodynamics written by Francesco Knechtli and published by Springer. This book was released on 2016-10-20 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the techniques central to lattice quantum chromodynamics, including modern developments. The book has four chapters. The first chapter explains the formulation of quarks and gluons on a Euclidean lattice. The second chapter introduces Monte Carlo methods and details the numerical algorithms to simulate lattice gauge fields. Chapter three explains the mathematical and numerical techniques needed to study quark fields and the computation of quark propagators. The fourth chapter is devoted to the physical observables constructed from lattice fields and explains how to measure them in simulations. The book is aimed at enabling graduate students who are new to the field to carry out explicitly the first steps and prepare them for research in lattice QCD.
Download or read book Modern Perspectives in Lattice QCD Quantum Field Theory and High Performance Computing written by Laurent Lellouch and published by OUP Oxford. This book was released on 2011-08-25 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is based on the lectures delivered at the XCIII Session of the École de Physique des Houches, held in August, 2009. The aim of the event was to familiarize the new generation of PhD students and postdoctoral fellows with the principles and methods of modern lattice field theory, which aims to resolve fundamental, non-perturbative questions about QCD without uncontrolled approximations. The emphasis of the book is on the theoretical developments that have shaped the field in the last two decades and that have turned lattice gauge theory into a robust approach to the determination of low energy hadronic quantities and of fundamental parameters of the Standard Model. By way of introduction, the lectures begin by covering lattice theory basics, lattice renormalization and improvement, and the many faces of chirality. A later course introduces QCD at finite temperature and density. A broad view of lattice computation from the basics to recent developments was offered in a corresponding course. Extrapolations to physical quark masses and a framework for the parameterization of the low-energy physics by means of effective coupling constants is covered in a lecture on chiral perturbation theory. Heavy-quark effective theories, an essential tool for performing the relevant lattice calculations, is covered from its basics to recent advances. A number of shorter courses round out the book and broaden its purview. These included recent applications to the nucleon—nucleon interation and a course on physics beyond the Standard Model.
Download or read book Strong coupling expansion for scattering phases in Hamiltonian lattice field theories written by Bernd Dahmen and published by . This book was released on 1994 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Progress in Gauge Field Theory written by G. 't Hooft and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: The importance of gauge theory for elementary particle physics is by now firmly established. Recent experiments have yielded convincing evidence for the existence of intermediate bosons, the carriers of the electroweak gauge force, as well as for the presence of gluons, the carriers of the strong gauge force, in hadronic interactions. For the gauge theory of strong interactions, however, a number of important theoretical problems remain to be definitely resolved. They include the quark confinement problem, the quantitative study of the hadron mass spectrum as well as the role of topology in quantum gauge field theory. These problems require for their solution the development and application of non-perturbative methods in quantum gauge field theory. These problems, and their non-perturbative analysis, formed the central interest of the 1983 Cargese summer institute on "Progress in Gauge Field Theory. " In this sense it was a natural sequel to the 1919 Cargese summer institute on "Recent Developments in Gauge Theories. " Lattice gauge theory provides a systematic framework for the investigation of non-perturbative quantum effects. Accordingly, a large number of lectures dealt with lattice gauge theory. Following a systematic introduction to the subject, the renormalization group method was developed both as a rigorous tool for fundamental questions, and in the block-spin formulation, the computations by Monte Carlo programs. A detailed analysis was presented of the problems encountered in computer simulations. Results obtained by this method on the mass spectrum were reviewed.
Download or read book Nuclear Lattice Effective Field Theory written by Timo A. Lähde and published by Springer. This book was released on 2019-05-07 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer begins with a brief introduction to the main ideas underlying Effective Field Theory (EFT) and describes how nuclear forces are obtained from first principles by introducing a Euclidean space-time lattice for chiral EFT. It subsequently develops the related technical aspects by addressing the two-nucleon problem on the lattice and clarifying how it fixes the numerical values of the low-energy constants of chiral EFT. In turn, the spherical wall method is introduced and used to show how improved lattice actions render higher-order corrections perturbative. The book also presents Monte Carlo algorithms used in actual calculations. In the last part of the book, the Euclidean time projection method is introduced and used to compute the ground-state properties of nuclei up to the mid-mass region. In this context, the construction of appropriate trial wave functions for the Euclidean time projection is discussed, as well as methods for determining the energies of the low-lying excitations and their spatial structure. In addition, the so-called adiabatic Hamiltonian, which allows nuclear reactions to be precisely calculated, is introduced using the example of alpha-alpha scattering. In closing, the book demonstrates how Nuclear Lattice EFT can be extended to studies of unphysical values of the fundamental parameters, using the triple-alpha process as a concrete example with implications for the anthropic view of the Universe. Nuclear Lattice Effective Field Theory offers a concise, self-contained, and introductory text suitable for self-study use by graduate students and newcomers to the field of modern computational techniques for atomic nuclei and nuclear reactions.
Download or read book Lattice Gauge Theories An Introduction Second Edition written by Heinz J Rothe and published by World Scientific Publishing Company. This book was released on 1997-06-09 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to an area of elementary particle physics which has been the subject of intensive research in the past two decades. It provides graduate students with the basic theoretical background on quantum gauge field theories formulated on a space-time lattice, and with the computational tools for carrying out research in this field. The book is a substantially extended version of the first edition which appeared in 1992. Much effort has been invested to present the material in a transparent way, and in exemplifying subtle points in simple models. The material covered should enable the reader to follow the vast literature on the subject without too much difficulties. Hopefully the book will motivate young physicists to carry out research in this area of elementary particle physics.
