New Spaces In Physics

Author by : Mathieu Anel
Languange : en
Publisher by : Cambridge University Press
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Description : After the development of manifolds and algebraic varieties in the previous century, mathematicians and physicists have continued to advance concepts of space. This book and its companion explore various new notions of space, including both formal and conceptual points of view, as presented by leading experts at the New Spaces in Mathematics and Physics workshop held at the Institut Henri Poincaré in 2015. This volume covers a broad range of topics in mathematical physics, including noncommutative geometry, supergeometry, derived symplectic geometry, higher geometric quantization, intuitionistic quantum logic, problems with the continuum description of spacetime, twistor theory, loop quantum gravity, and geometry in string theory. It is addressed primarily to mathematical physicists and mathematicians, but also to historians and philosophers of these disciplines.


Renormalization Group

Author by : Giuseppe Benfatto
Languange : en
Publisher by : Princeton University Press
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Description : Scaling and self-similarity ideas and methods in theoretical physics have, in the last twenty-five years, coalesced into renormalization-group methods. This book analyzes, from a single perspective, some of the most important applications: the critical-point theory in classical statistical mechanics, the scalar quantum field theories in two and three space-time dimensions, and Tomonaga's theory of the ground state of one-dimensional Fermi systems. The dimension dependence is discussed together with the related existence of anomalies (in Tomonaga's theory and in 4 -e dimensions for the critical point). The theory of Bose condensation at zero temperature in three space dimensions is also considered. Attention is focused on results that can in principle be formally established from a mathematical point of view. The 4 -e dimensions theory, Bose condensation, as well as a few other statements are exceptions to this rule, because no complete treatment is yet available. However, the truly mathematical details are intentionally omitted and only referred to. This is done with the purpose of stressing the unifying conceptual structure rather than the technical differences or subtleties.


Renormalization

Author by : Manfred Salmhofer
Languange : en
Publisher by : Springer Science & Business Media
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Description : This monograph is the first to present the recently discovered renormalization techniques for the Schrödinger and Dirac equations, providing a mathematically rigorous, yet simple and clear introduction to the subject. It develops field-theoretic techniques such as Feynman graph expansions and renormalization, taking pains to make all proofs as simple as possible by using generating function techniques throughout. Renormalization is performed by using an exact renormalization group differential equation, a technique that provides simple but complete proofs of the theorems.


Mathematical Methods Of Many Body Quantum Field Theory

Author by : Detlef Lehmann
Languange : en
Publisher by : CRC Press
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Description : Mathematical Methods of Many-Body Quantum Field Theory offers a comprehensive, mathematically rigorous treatment of many-body physics. It develops the mathematical tools for describing quantum many-body systems and applies them to the many-electron system. These tools include the formalism of second quantization, field theoretical perturbation theo


Random Walks Critical Phenomena And Triviality In Quantum Field Theory

Author by : Roberto Fernandez
Languange : en
Publisher by : Springer Science & Business Media
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Description : Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.


Constructive Quantum Field Theory Ii

Author by : G. Velo
Languange : en
Publisher by : Springer Science & Business Media
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Description : The seventh Ettore Majorana International School of Mathematical Physics was :Jeld at the Centro della Cultura Scientifica Erice. Sicily, 1-15 July 1988. The present volume collects lecture notes on the session which was entitled Con8tructive Quantum Field Theory lI. The II refers to the fact that the first such school in 1973 was devoted ,0 the same subject. The school was a NATO Advanced Study Institute sponsored Jy the Italian Ministry of Scientific and Technological Research and the Regional 3icilian Government. At the time of the 1973 Erice School on Constructive Field Theory, the speakers :ould summarize a decade of effort on the solution of superrenormalizable models in two dimensional space-time leading to the verification of the axioms of relativistic :J. uantum field theory for these examples. The resulting lecture notes have proved ,0 be exceptionally useful and are still in print. In the decade and a half that have ~lapsed since that time, there has been much hard work with the ultimate objective of providing a rigorous mathematical foundation for the quantum field theories in four iimensional space-time that summarize a large fraction of our current understanding )f elementary particle physics: QCD and the electroweak theory. The lecture notes )f the 1988 school record the fact that, although this objective has not been reached, Important progress has been made. The ultraviolet stability of Yang-Mills theory In four dimensions has been treated and renormalizable (not superrenormalizable) models in two dimensional space-time, Gross-Neveu models, have been solved.


General Catalog

Author by : Georgia Institute of Technology
Languange : en
Publisher by : Unknown
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Synchrotron Radiation Sources

Author by : Herman Winick
Languange : en
Publisher by : World Scientific
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Description : Specialists in the technical components of a synchrotron light source are usually well versed in their field and in the associated technical literature. However, with the rapid and continuing growth of synchrotron radiation research, and with new facilities coming online and being authorized for design and construction around the world, there is a need for a reference book that describes the various technical components of a synchrotron light source in a manner that will be useful to those who lack specialized technical background, but who have responsibility for some part of the design, construction, operation or development of such a facility. This would include technicians, engineers and physicists who have technical background in related fields but no specific experience with a synchrotron light source, and also project managers, laboratory directors, and government officials involved with synchrotron light facilities.College level scientific or engineering training or the equivalent experience is assumed and appropriate mathematics is used throughout. However, the basic concepts in each chapter are given in less technical language and a glossary of terms as well as an index will make the book useful for those with less technical training or experience.


Properties And Interactions Of Interplanetary Dust

Author by : L. Giese
Languange : en
Publisher by : Springer Science & Business Media
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Description : Investigation of the interplanetary dust cloud is characterized by contributions from quite different methods and fields, such as research on zodiacal light, meteors, micrometeoroids, asteroids, and comets. Since the earth's environment and interplanetary space became accessible to space vehicles these interrelations are clearly evident and extremely useful. Space measurements by micrometeoroid detectors, for example, provide individual and eventually detailed information on impact events, which however are limited in number and therefore restricted in statistical significance. On the other hand, zodiacal light measurements involve scattered light from many particles and therefore provide global information about the average values of physical properties and spatial distribution of interplanetary grains. Additional knowledge stems from lunar samples and from dust collections in the atmosphere and in deep sea sediments. All these sources of complementary information must be put together into a synoptical synthesis. This also has to take into account dynamical aspects and the results of laboratory investigations concerning physical properties of small grains. Such considerable effort is not merely an academic exercise for a few specialists interested in the solar dust cloud. Since this same cloud exclusively allows direct in-situ acess to investigate extraterrestrial dust particles over a wide range of sizes and materials, it provides valuable information for realistic treatment of dust phenomena in other remote cosmic regions such as in dense molecular clouds, circumstellar dust shells, and even protostellar or protoplanetary systems.


Lecture Notes On The Discretization Of The Boltzmann Equation

Author by : Nicola Bellomo
Languange : en
Publisher by : World Scientific
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Description : This book presents contributions on the following topics: discretization methods in the velocity and space, analysis of the conservation properties, asymptotic convergence to the continuous equation when the number of velocities tends to infinity, and application of discrete models. It consists of ten chapters. Each chapter is written by applied mathematicians who have been active in the field, and whose scientific contributions are well recognized by the scientific community. Contents:From the Boltzmann Equation to Discretized Kinetic Models (N Bellomo & R Gatignol)Discrete Velocity Models for Gas Mixtures (C Cercignani)Discrete Velocity Models with Multiple Collisions (R Gatignol)Discretization of the Boltzmann Equation and the Semicontinuous Model (L Preziosi & L Rondoni)Semi-continuous Extended Kinetic Theory (W Koller)Steady Kinetic Boundary Value Problems (H Babovsky et al.)Computational Methods and Fast Algorithms for the Boltzmann Equation (L Pareschi)Discrete Velocity Models and Dynamical Systems (A Bobylev & N Bernhoff)Numerical Method for the Compton Scattering Operator (C Buet & S Cordier)Discrete Models of the Boltzmann Equation in Quantum Optics and Arbitrary Partition of the Velocity Space (F Schürrer) Readership: Higher level postgraduates in applied mathematics. Keywords:Boltzmann Equation;Discrete Velocity Models;Evolution of a System of Equal Particles;Discretization Methods;Asymptotic Convergence;Initial/Boundary ConditionsReviews:“This book is a collection of high quality and very interesting articles dedicated to Henri Cabannes, one of the pioneers and prime movers of discrete kinetic theory, on the occasion of his 80th birthday … This is a really nice collection of articles and will be a very useful reference for some time to come.”Mathematical Reviews “This is a really nice collection of articles and will be a very useful reference for some time to come.”Zentralblatt MATH


Statistical Dynamics

Author by : R. F. Streater
Languange : en
Publisher by : Imperial College Press
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Description : How can one construct dynamical systems obeying the first and second laws of thermodynamics: mean energy is conserved and entropy increases with time? This book answers the question for classical probability (Part I) and quantum probability (Part II). A novel feature is the introduction of heat particles which supply thermal noise and represent the kinetic energy of the molecules. When applied to chemical reactions, the theory leads to the usual nonlinear reaction-diffusion equations as well as modifications of them. These can exhibit oscillations, or can converge to equilibrium.In this second edition, the text is simplified in parts and the bibliography has been expanded. The main difference is the addition of two new chapters; in the first, classical fluid dynamics is introduced. A lattice model is developed, which in the continuum limit gives us the Euler equations. The five Navier-Stokes equations are also presented, modified by a diffusion term in the continuity equation. The second addition is in the last chapter, which now includes estimation theory, both classical and quantum, using information geometry.


Encyclopaedia Of Mathematics

Author by : Michiel Hazewinkel
Languange : en
Publisher by : Springer Science & Business Media
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Description : This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.


High Energy Physics Index

Author by : Anonim
Languange : en
Publisher by : Unknown
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Higher Homotopy Structures In Topology And Mathematical Physics

Author by : James D. Stasheff
Languange : en
Publisher by : American Mathematical Soc.
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Description : Since the work of Stasheff and Sugawara in the 1960s on recognition of loop space structures on $H$-spaces, the notion of higher homotopies has grown to be a fundamental organizing principle in homotopy theory, differential graded homological algebra and even mathematical physics. This book presents the proceedings from a conference held on the occasion of Stasheff's 60th birthday at Vassar in June 1996. It offers a collection of very high quality papers and includes some fundamental essays on topics that open new areas. It's features include: accessible to a broad audience interested in mathematics and physics; offers a comprehensive overview of Stasheff's work; and, contains papers on very current research topics, including operads, combinatorial polyhedra and moduli spaces.


Supersymmetry

Author by : S Ferrara
Languange : en
Publisher by : World Scientific
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Description : Readership: High energy physicists, nuclear physicists, mathematicians and mathematical physicists. Keywords:Supersymmetry;Supergravity;Super-Higgs Effect;High Energy Physics


Applied Micromechanics Of Porous Materials

Author by : Luc Dormieux
Languange : en
Publisher by : Springer Science & Business Media
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Description : Poromechanics is the mechanics of porous materials and is now a well established field in many engineering disciplines, ranging from Civil Engineering, Geophysics, Petroleum Engineering to Bioengineering. However, a rigorous approach that links the physics of the phenomena at stake in porous materials and the macroscopic behaviour is still missing. This book presents such an approach by means of homogenization techniques. Rigorously founded in various theories of micromechanics, these up scaling techniques are developed for the homogenization of transport properties, stiffness and strength properties of porous materials. The special feature of this book is the balance between theory and application, providing the reader with a comprehensive introduction to state-of-the-art homogenization theories and applications to a large range of real life porous materials: concrete, rocks, shales, bones, etc.


Lectures On Probability Theory And Statistics

Author by : Sergio Albeverio
Languange : en
Publisher by : Springer Science & Business Media
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Description : In World Mathematical Year 2000 the traditional St. Flour Summer School was hosted jointly with the European Mathematical Society. Sergio Albeverio reviews the theory of Dirichlet forms, and gives applications including partial differential equations, stochastic dynamics of quantum systems, quantum fields and the geometry of loop spaces. The second text, by Walter Schachermayer, is an introduction to the basic concepts of mathematical finance, including the Bachelier and Black-Scholes models. The fundamental theorem of asset pricing is discussed in detail. Finally Michel Talagrand, gives an overview of the mean field models for spin glasses. This text is a major contribution towards the proof of certain results from physics, and includes a discussion of the Sherrington-Kirkpatrick and the p-spin interaction models.


Modern Classical Optics

Author by : Geoffrey Brooker
Languange : en
Publisher by : Oxford University Press
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Description : The book describes classical (non-quantum) optical phenomena and the instruments and technology based on them. It includes many cutting-edge areas of modern physics and its applications which are not covered in many larger and more expensive books.


Lattice 92

Author by : Jan Smit
Languange : en
Publisher by : Unknown
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Neutron Scattering Magnetic And Quantum Phenomena

Author by : Anonim
Languange : en
Publisher by : Elsevier
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Description : Neutron Scattering - Magnetic and Quantum Phenomena provides detailed coverage of the application of neutron scattering in condensed matter research. The book's primary aim is to enable researchers in a particular area to identify the aspects of their work where neutron scattering techniques might contribute, conceive the important experiments to be done, assess what is required to carry them out, write a successful proposal for one of the major user facilities, and perform the experiments under the guidance of the appropriate instrument scientist. An earlier series edited by Kurt Sköld and David L. Price, and published in the 1980s by Academic Press as three volumes in the series Methods of Experimental Physics, was very successful and remained the standard reference in the field for several years. This present work has similar goals, taking into account the advances in experimental techniques over the past quarter-century, for example, neutron reflectivity and spin-echo spectroscopy, and techniques for probing the dynamics of complex materials of technological relevance. This volume complements Price and Fernandez-Alonso (Eds.), Neutron Scattering - Fundamentals published in November 2013. Covers the application of neutron scattering techniques in the study of quantum and magnetic phenomena, including superconductivity, multiferroics, and nanomagnetism Presents up-to-date reviews of recent results, aimed at enabling the reader to identify new opportunities and plan neutron scattering experiments in their own field Provides a good balance between theory and experimental techniques Provides a complement to Price and Fernandez-Alonso (Eds.), Neutron Scattering - Fundamentals published in November 2013


Effective Spacetime

Author by : Karen Crowther
Languange : en
Publisher by : Springer
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Description : This book discusses the notion that quantum gravity may represent the "breakdown" of spacetime at extremely high energy scales. If spacetime does not exist at the fundamental level, then it has to be considered "emergent", in other words an effective structure, valid at low energy scales. The author develops a conception of emergence appropriate to effective theories in physics, and shows how it applies (or could apply) in various approaches to quantum gravity, including condensed matter approaches, discrete approaches, and loop quantum gravity.


Lattice

Author by : Anonim
Languange : en
Publisher by : Unknown
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Multigrid Methods Ii

Author by : Wolfgang Hackbusch
Languange : en
Publisher by : Springer
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Open Quantum Systems Ii

Author by : Stéphane Attal
Languange : en
Publisher by : Springer
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Total Read : 19
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Description : Understanding dissipative dynamics of open quantum systems remains a challenge in mathematical physics. This problem is relevant in various areas of fundamental and applied physics. Significant progress in the understanding of such systems has been made recently. These books present the mathematical theories involved in the modeling of such phenomena. They describe physically relevant models, develop their mathematical analysis and derive their physical implications.


Nuovo Cimento

Author by : Anonim
Languange : en
Publisher by : Unknown
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Stochastic Global Optimization

Author by : Anatoly Zhigljavsky
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 30
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Description : This book examines the main methodological and theoretical developments in stochastic global optimization. It is designed to inspire readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods. Among the book’s features is a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms.


Peyresq Lectures On Nonlinear Phenomena

Author by : Freddy Bouchet
Languange : en
Publisher by : World Scientific
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Total Read : 29
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Description : This book is the third volume of lecture notes from summer schools held in the small village of Peyresq (France). These lectures cover nonlinear physics in a broad sense. They were given over the period 2004 to 2008. The summer schools were organized by the Institut Non Lin(r)aire de Nice (Nice, France), the Laboratoire de Physique Statistique (ENS Paris, France) and the Institut de Recherche de Physique Hors Equilibre (Marseilles, France). The goal of the book is to provide a high-quality overview on the state of the art in nonlinear sciences, and to promote the transfer of knowledge between the various domains in physics dealing with nonlinear phenomen