Local Quantum Physics

Fields, Particles, Algebras

Author: Rudolf Haag

Publisher: Springer Science & Business Media

ISBN: 3642614582

Category: Science

Page: 392

View: 5539

The new edition provided the opportunity of adding a new chapter entitled "Principles and Lessons of Quantum Physics". It was a tempting challenge to try to sharpen the points at issue in the long lasting debate on the Copenhagen Spirit, to assess the significance of various arguments from our present vantage point, seventy years after the advent of quantum theory, where, after ali, some problems appear in a different light. It includes a section on the assumptions leading to the specific mathematical formalism of quantum theory and a section entitled "The evolutionary picture" describing my personal conclusions. Alto gether the discussion suggests that the conventional language is too narrow and that neither the mathematical nor the conceptual structure are built for eter nity. Future theories will demand radical changes though not in the direction of a return to determinism. Essential lessons taught by Bohr will persist. This chapter is essentially self-contained. Some new material has been added in the last chapter. It concerns the char acterization of specific theories within the general frame and recent progress in quantum field theory on curved space-time manifolds. A few pages on renor malization have been added in Chapter II and some effort has been invested in the search for mistakes and unclear passages in the first edition. The central objective of the book, expressed in the title "Local Quantum Physics", is the synthesis between special relativity and quantum theory to gether with a few other principles of general nature.

Reality and Measurement in Algebraic Quantum Theory

NWW 2015, Nagoya, Japan, March 9-13

Author: Masanao Ozawa,Jeremy Butterfield,Hans Halvorson,Miklós Rédei,Yuichiro Kitajima,Francesco Buscemi

Publisher: Springer

ISBN: 9811324875

Category: Mathematics

Page: 396

View: 5395

This volume contains papers based on presentations at the “Nagoya Winter Workshop 2015: Reality and Measurement in Algebraic Quantum Theory (NWW 2015)”, held in Nagoya, Japan, in March 2015. The foundations of quantum theory have been a source of mysteries, puzzles, and confusions, and have encouraged innovations in mathematical languages to describe, analyze, and delineate this wonderland. Both ontological and epistemological questions about quantum reality and measurement have been placed in the center of the mysteries explored originally by Bohr, Heisenberg, Einstein, and Schrödinger. This volume describes how those traditional problems are nowadays explored from the most advanced perspectives. It includes new research results in quantum information theory, quantum measurement theory, information thermodynamics, operator algebraic and category theoretical foundations of quantum theory, and the interplay between experimental and theoretical investigations on the uncertainty principle. This book is suitable for a broad audience of mathematicians, theoretical and experimental physicists, and philosophers of science.

Quantum Field Theory II: Quantum Electrodynamics

A Bridge between Mathematicians and Physicists

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 3540853774

Category: Mathematics

Page: 1101

View: 3165

And God said, Let there be light; and there was light. Genesis 1,3 Light is not only the basis of our biological existence, but also an essential source of our knowledge about the physical laws of nature, ranging from the seventeenth century geometrical optics up to the twentieth century theory of general relativity and quantum electrodynamics. Folklore Don’t give us numbers: give us insight! A contemporary natural scientist to a mathematician The present book is the second volume of a comprehensive introduction to themathematicalandphysicalaspectsofmodernquantum?eldtheorywhich comprehends the following six volumes: Volume I: Basics in Mathematics and Physics Volume II: Quantum Electrodynamics Volume III: Gauge Theory Volume IV: Quantum Mathematics Volume V: The Physics of the Standard Model Volume VI: Quantum Gravitation and String Theory. It is our goal to build a bridge between mathematicians and physicists based on the challenging question about the fundamental forces in • macrocosmos (the universe) and • microcosmos (the world of elementary particles). The six volumes address a broad audience of readers, including both und- graduate and graduate students, as well as experienced scientists who want to become familiar with quantum ?eld theory, which is a fascinating topic in modern mathematics and physics.

General Principles of Quantum Field Theory

Author: N.N. Bogolubov,Anatoly A. Logunov,A.I. Oksak,I. Todorov

Publisher: Springer Science & Business Media

ISBN: 9400904916

Category: Science

Page: 695

View: 8001

The majority of the "memorable" results of relativistic quantum theory were obtained within the framework of the local quantum field approach. The explanation of the basic principles of the local theory and its mathematical structure has left its mark on all modern activity in this area. Originally, the axiomatic approach arose from attempts to give a mathematical meaning to the quantum field theory of strong interactions (of Yukawa type). The fields in such a theory are realized by operators in Hilbert space with a positive Poincare-invariant scalar product. This "classical" part of the axiomatic approach attained its modern form as far back as the sixties. * It has retained its importance even to this day, in spite of the fact that nowadays the main prospects for the description of the electro-weak and strong interactions are in connection with the theory of gauge fields. In fact, from the point of view of the quark model, the theory of strong interactions of Wightman type was obtained by restricting attention to just the "physical" local operators (such as hadronic fields consisting of ''fundamental'' quark fields) acting in a Hilbert space of physical states. In principle, there are enough such "physical" fields for a description of hadronic physics, although this means that one must reject the traditional local Lagrangian formalism. (The connection is restored in the approximation of low-energy "phe nomenological" Lagrangians.

Quantum Mathematical Physics

A Bridge between Mathematics and Physics

Author: Felix Finster,Johannes Kleiner,Christian Röken,Jürgen Tolksdorf

Publisher: Birkhäuser

ISBN: 331926902X

Category: Science

Page: 518

View: 5658

Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

Advances in Algebraic Quantum Field Theory

Author: Romeo Brunetti,Claudio Dappiaggi,Klaus Fredenhagen,Jakob Yngvason

Publisher: Springer

ISBN: 3319213539

Category: Science

Page: 453

View: 1682

This text focuses on the algebraic formulation of quantum field theory, from the introductory aspects to the applications to concrete problems of physical interest. The book is divided in thematic chapters covering both introductory and more advanced topics. These include the algebraic, perturbative approach to interacting quantum field theories, algebraic quantum field theory on curved spacetimes (from its structural aspects to the applications in cosmology and to the role of quantum spacetimes), algebraic conformal field theory, the Kitaev's quantum double model from the point of view of local quantum physics and constructive aspects in relation to integrable models and deformation techniques. The book is addressed to master and graduate students both in mathematics and in physics, who are interested in learning the structural aspects and the applications of algebraic quantum field theory.

Lattice Statistics and Mathematical Physics

Proceedings of the APCTP-NANKAI Joint Symposium : Festschrift Dedicated to Professor Fa-Yueh Wu on the Occasion of His 70th Birthday : Tianjin, China, 7-11 October, 2001

Author: Jacques H. H. Perk

Publisher: World Scientific

ISBN: 9789812776358

Category: Science

Page: 328

View: 9116

This book contains thirty-six short papers on recent progress in a variety of subjects in mathematical and theoretical physics, written for the proceedings of a symposium in honor of the seventieth birthday of Professor F Y Wu, held at the Nankai Institute of Mathematics, October 7OCo11, 2001. The collection of papers is aimed at researchers, including graduate students, with an interdisciplinary interest and gives a brief introduction to many of the topics of current interest. These include new results on exactly solvable models in statistical mechanics, integrable through the YangOCoBaxter equations, quantum groups, fractional statistics, random matrices, index theorems on the lattice, combinatorics, and other related topics."

Compendium of Quantum Physics

Concepts, Experiments, History and Philosophy

Author: Daniel Greenberger,Klaus Hentschel,Friedel Weinert

Publisher: Springer Science & Business Media

ISBN: 9783540706267

Category: Science

Page: 901

View: 794

With contributions by leading quantum physicists, philosophers and historians, this comprehensive A-to-Z of quantum physics provides a lucid understanding of key concepts of quantum theory and experiment. It covers technical and interpretational aspects alike, and includes both traditional and new concepts, making it an indispensable resource for concise, up-to-date information about the many facets of quantum physics.

Relativität, Gruppen, Teilchen

Spezielle Relativitätstheorie als Grundlage der Feld- und Teilchenphysik

Author: R.U. Sexl,H.K. Urbantke

Publisher: Springer-Verlag

ISBN: 3709122465

Category: Science

Page: 301

View: 8275

Quantum Field Theory and Gravity

Conceptual and Mathematical Advances in the Search for a Unified Framework

Author: Felix Finster,Olaf Müller,Marc Nardmann,Jürgen Tolksdorf,Eberhard Zeidler

Publisher: Springer Science & Business Media

ISBN: 3034800436

Category: Mathematics

Page: 382

View: 9206

One of the most challenging problems of contemporary theoretical physics is the mathematically rigorous construction of a theory which describes gravitation and the other fundamental physical interactions within a common framework. The physical ideas which grew from attempts to develop such a theory require highly advanced mathematical methods and radically new physical concepts. This book presents different approaches to a rigorous unified description of quantum fields and gravity. It contains a carefully selected cross-section of lively discussions which took place in autumn 2010 at the fifth conference "Quantum field theory and gravity - Conceptual and mathematical advances in the search for a unified framework" in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

Introduction to Symmetry and Supersymmetry in Quantum Field Theory

Author: J Lopuszanski

Publisher: World Scientific

ISBN: 9814507717

Category:

Page: 388

View: 6075

This is a set of lecture notes given by the author at the Universities of Göttingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one-semester course for graduate students in the field of mathematical physics and high energy physics. Contents:IntroductionExample of a Classical and Quantum Scalar Free Field TheoryScene and Subject of the Drama. Axiom 1 and 2Subject of the DramaPrinciple of Relativity. Causality. Axiom 3, 4 and 5Irreducibility of the Field Algebra and the Scattering Theory. Axiom 6. Axiom 0Preliminaries about Physical SymmetriesCurrents and ChargesGlobal Symmetries and Supersymmetries of the S-MatrixRepresentations of the Super-Lie AlgebraThe Case of Massless ParticlesFermionic ChargesConcluding Remarks Readership: Mathematical physicists and high energy physicists. Keywords:Symmetry in Physics;Supersymmetry;Quantum Field Theory;Relativity;Spinors;SL(2,C) Group;Symplectic Space;Scalar Charges;Vector Charges;Supercharges;Central Charges;Representation of the Super Lie Algebra;Currents;S-Matrix Coleman — Mandula Theorem;Scattering Theory Coleman — Mandula Theorem

The Neumann Compendium

Author: John Von Neumann,F. Br¢dy,Tibor V mos

Publisher: World Scientific

ISBN: 9789810222017

Category: Mathematics

Page: 699

View: 4373

After three decades since the first nearly complete edition of John von Neumann's papers, this book is a valuable selection of those papers and excerpts of his books that are most characteristic of his activity, and reveal that of his continuous influence.The results receiving the 1994 Nobel Prizes in economy deeply rooted in Neumann's game theory are only minor traces of his exceptionally broad spectrum of creativity and stimulation.The book is organized by the specific subjects-quantum mechanics, ergodic theory, operator algebra, hydrodynamics, economics, computers, science and society. In addition, one paper which was written in German will be translated and published in English for the first time.The sections are introduced by short explanatory notes with an emphasis on recent developments based on von Neumann's contributions. An overall picture is provided by Ulam's, one of his most intimate partners in thinking, 1958 memorial lecture. Facsimilae and translations of some of his personal letters and a newly completed bibliography based on von Neumann's own careful compilation are added.

An Introduction to Symmetry and Supersymmetry in Quantum Field Theory

Author: Jan T. ?opusza?ski

Publisher: World Scientific

ISBN: 9789971501617

Category: Science

Page: 373

View: 6313

This is a set of lecture notes given by the author at the Universities of G”ttingen and Wroclaw. The text presents the axiomatic approach to field theory and studies in depth the concepts of symmetry and supersymmetry and their associated generators, currents and charges. It is intended as a one-semester course for graduate students in the field of mathematical physics and high energy physics.

Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics

Author: K.H. Namsrai

Publisher: Springer Science & Business Media

ISBN: 9400945183

Category: Science

Page: 426

View: 7981

over this stochastic space-time leads to the non local fields considered by G. V. Efimov. In other words, stochasticity of space-time (after being averaged on a large scale) as a self-memory makes the theory nonlocal. This allows one to consider in a unified way the effect of stochasticity (or nonlocality) in all physical processes. Moreover, the universal character of this hypothesis of space-time at small distances enables us to re-interpret the dynamics of stochastic particles and to study some important problems of the theory of stochastic processes [such as the relativistic description of diffusion, Feynman type processes, and the problem of the origin of self-turbulence in the motion of free particles within nonlinear (stochastic) mechanics]. In this direction our approach (Part II) may be useful in recent developments of the stochastic interpretation of quantum mechanics and fields due to E. Nelson, D. Kershaw, I. Fenyes, F. Guerra, de la Pena-Auerbach, J. -P. Vigier, M. Davidson, and others. In particular, as shown by N. Cufaro Petroni and J. -P. Vigier, within the discussed approach, a causal action-at-distance interpretation of a series of experiments by A. Aspect and his co-workers indicating a possible non locality property of quantum mechanics, may also be obtained. Aspect's results have recently inspired a great interest in different nonlocal theories and models devoted to an understanding of the implications of this nonlocality. This book consists of two parts.

Diffusion, Quantum Theory, and Radically Elementary Mathematics

Author: William G. Faris

Publisher: N.A

ISBN: 9780691125459

Category: Mathematics

Page: 243

View: 8376

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

Symmetry in Mathematics and Physics

Conference in Honor of V.S. Varadarajan's Birthday, January 18-20, 2008, University of California, Los Angeles, California

Author: Donald G. Babbitt,Vyjayanthi Chari,Rita Fioresi

Publisher: American Mathematical Soc.

ISBN: 0821847317

Category: Science

Page: 250

View: 7119

The articles in this volume mainly grew out of talks given at a Conference held at UCLA in January 2008, which honored V. S. Varadarajan on his 70th birthday. The main theme of the Conference was symmetry in mathematics and physics, areas of mathematics and mathematical physics in which Varadarajan has made significant contributions during the past 50 years. Very early in his career he also worked and made significant contributions in the areas of probability and the foundations of quantum mechanics. Topics covered by the articles in this volume are probability, quantum mechanics, symmetry (broadly interpreted in mathematics and physics), finite and infinite dimensional Lie groups and Lie algebras and their representations, super Lie groups and supergeometry (relatively new but active and important fields at the interface between mathematics and physics), and supersymmetry. The latter topic takes on a special importance since one of the first experiments at the Large Hadron Collider at CERN will be a test of whether supersymmetry exists in the world of elementary particles. A reprint of an exposition of supersymmetry by one of its founders, B. Zumino, appears in this volume.

Relativistic Quantum Mechanics of Leptons and Fields

Author: W.T. Grandy

Publisher: Springer Science & Business Media

ISBN: 9780792310495

Category: Science

Page: 438

View: 1021

The material contained in this work concerns relativistic quantum mechanics, and as such pertains to classical fields. On the one hand it is meant to serve as a text on the subject, a desire stemming from the author's fruitless searches for an adequate, up-to-date reference when lecturing on these topics. At times the supplementary material was found to exceed by far that in the assigned text. On the other hand, there is some flavor of a monograph to what follows, most particularly in the later chapters, for a major goal is to demonstrate just how far we can advance our understanding of the behavior of stable particles and their interactions without introducing quantized fields. Those wishing to describe the world in this way may view the result as a point of departure, despite the fact that their wish remains unfulfilled. Confirmed quantum-field theorists, however, will doubtless view it as a summary of just why they feel compelled to quantize the fields. Approximately half the book is devoted to the single-particle Dirac equation and its solutions. A great deal of detail is provided in this respect, and the discus sion is reasonably comprehensive. The Dirac equation is extraordinarily important in its own right, particularly as a basis for quantum electrodynamics (QED), and is thus worthy of extensive study.

Diverse Topics in Theoretical and Mathematical Physics

Author: Roman W. Jackiw

Publisher: World Scientific

ISBN: 9789810216979

Category: Science

Page: 514

View: 7048

In this volume, topics are drawn from field theory, especially gauge field theory, as applied to particle, condensed matter and gravitational physics, and concern a variety of interesting subjects. These include geometricalDtopological effects in quantum theory, fractional charge, time travel, relativistic quantized fields in and out of thermal equilibrium and quantum modifications of symmetry in physical systems.Many readers will find this a useful volume, especially theoretical physicists and mathematicians. The material will be of interest to both the expert who will find well-presented novel and stimulating viewpoints of various subjects and the novice who will find complete, detailed and precise descriptions of important topics of current interest, in theoretical and mathematical physics.