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Author: Timo A. Lähde Publisher: Springer ISBN: 3030141896 Category : Science Languages : en Pages : 400
Book Description
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.
Author: Timo A. Lähde Publisher: Springer ISBN: 3030141896 Category : Science Languages : en Pages : 400
Book Description
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.
Author: Heinz J Rothe Publisher: World Scientific ISBN: 9814602302 Category : Languages : en Pages : 397
Book Description
This book introduces a large number of topics in lattice gauge theories, including analytical as well as numerical methods. It provides young physicists with the theoretical background and basic computational tools in order to be able to follow the extensive literature on the subject, and to carry out research on their own. Whenever possible, the basic ideas and technical inputs are demonstrated in simple examples, so as to avoid diverting the readers' attention from the main line of thought. Sufficient technical details are however given so that he can fill in the remaining details with the help of the cited literature without too much effort.This volume is designed for graduate students in theoretical elementary particle physics or statistical mechanics with a basic knowledge in Quantum Field Theory.
Author: Christof Gattringer Publisher: Springer ISBN: 3642018505 Category : Science Languages : en Pages : 352
Book Description
This introduction to quantum chromodynamics presents the basic concepts and calculations in a clear and didactic style accessible to those new to the field. Readers will find useful methods for obtaining numerical results, including pure gauge theory and quenched spectroscopy.
Author: Claude Itzykson Publisher: Cambridge University Press ISBN: 9780521408059 Category : Science Languages : en Pages : 440
Book Description
Volume 1: From Brownian Motion to Renormalization and Lattice Gauge Theory. Volume 2: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. This two-volume work provides a comprehensive and timely survey of the application of the methods of quantum field theory to statistical physics, a very active and fruitful area of modern research. The first volume provides a pedagogical introduction to the subject, discussing Brownian motion, its anticommutative counterpart in the guise of Onsager's solution to the two-dimensional Ising model, the mean field or Landau approximation, scaling ideas exemplified by the Kosterlitz-Thouless theory for the XY transition, the continuous renormalization group applied to the standard phi-to the fourth theory (the simplest typical case) and lattice gauge theory as a pathway to the understanding of quark confinement in quantum chromodynamics. The second volume covers more diverse topics, including strong coupling expansions and their analysis, Monte Carlo simulations, two-dimensional conformal field theory, and simple disordered systems. The book concludes with a chapter on random geometry and the Polyakov model of random surfaces which illustrates the relations between string theory and statistical physics. The two volumes that make up this work will be useful to theoretical physicists and applied mathematicians who are interested in the exciting developments which have resulted from the synthesis of field theory and statistical physics.
Author: Robert Oeckl Publisher: Imperial College Press ISBN: 1860947379 Category : Science Languages : en Pages : 218
Book Description
This book provides an introduction to topological quantum field theory as well as discrete gauge theory with quantum groups. In contrast to much of the existing literature, the present approach is at the same time intuitive and mathematically rigorous, making extensive use of suitable diagrammatic methods. It provides a highly unified description of lattice gauge theory, topological quantum field theory and models of quantum (super)gravity. The reader is thus in a unique position to understand the relations between these subjects as well as the underlying groundwork.
Author: Tamas S Biro Publisher: World Scientific ISBN: 9814501158 Category : Science Languages : en Pages : 300
Book Description
This book introduces a rapidly growing new research area — the study of dynamical properties of elementary fields. The methods used in this field range from algebraic topology to parallel computer programming. The main aim of this research is to understand the behavior of elementary particles and fields under extreme circumstances, first of all at high temperature and energy density generated in the largest accelerators of the world and supposed to be present in the early evolution of our Universe shortly after the Big Bang.In particular, chaos is rediscovered in a new appearance in these studies: in gauge theories the well-known divergence of initially adjacent phase space trajectories leads over into a quasi-thermal distribution of energy with a saturated average distance of different field configurations. This particular behavior is due to the compactness of the gauge group.Generally this book is divided into two main parts: the first part mainly deals with the “classical” discovery of chaos in gauge field theory while the second part presents methods and research achievements in recent years. One chapter is devoted entirely to the presentation and discussion of computational problems. The major theme, returning again and again throughout the book, is of course the phenomenon with a thousand faces — chaos itself.This book is intended to be a research book which introduces the reader to a new research field, presenting the basic new ideas in detail but just briefly touching on the problems of other related fields, like perturbative or lattice gauge theory, or dissipative chaos. The terminology of these related fields are, however, used.Exercises are also included in this book. They deepen the reader's understanding of special issues and at the same time offer more information on related problems. For the convenience of the fast reader, solutions are presented right after the problems.
Author: Huey-Wen Lin Publisher: Springer ISBN: 3319080229 Category : Science Languages : en Pages : 255
Book Description
With ever increasing computational resources and improvements in algorithms, new opportunities are emerging for lattice gauge theory to address key questions in strongly interacting systems, such as nuclear matter. Calculations today use dynamical gauge-field ensembles with degenerate light up/down quarks and the strange quark and it is possible now to consider including charm-quark degrees of freedom in the QCD vacuum. Pion masses and other sources of systematic error, such as finite-volume and discretization effects, are beginning to be quantified systematically. Altogether, an era of precision calculation has begun and many new observables will be calculated at the new computational facilities. The aim of this set of lectures is to provide graduate students with a grounding in the application of lattice gauge theory methods to strongly interacting systems and in particular to nuclear physics. A wide variety of topics are covered, including continuum field theory, lattice discretizations, hadron spectroscopy and structure, many-body systems, together with more topical lectures in nuclear physics aimed a providing a broad phenomenological background. Exercises to encourage hands-on experience with parallel computing and data analysis are included.
Author: Timo A. Lähde
Author: Timo A. Lähde
Author: Jan Smit
Author: Istvan Montvay
Author: Heinz J Rothe
Author: Christof Gattringer
Author: Michael Creutz
Author: Claude Itzykson
Author: Robert Oeckl
Author: Tamas S Biro
Author: Huey-Wen Lin