Translation Group And Particle Representations In Quantum Field Theory

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Translation Group and Particle Representations in Quantum Field Theory

Author : Hans-Jürgen Borchers
Publisher : Springer
ISBN 13 : 9783662140789
Total Pages : 136 pages
Book Rating : 4.1/5 (47 download)

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Book Synopsis Translation Group and Particle Representations in Quantum Field Theory by : Hans-Jürgen Borchers

Download or read book Translation Group and Particle Representations in Quantum Field Theory written by Hans-Jürgen Borchers and published by Springer. This book was released on 2014-04-18 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the time I learned quantum field theory it was considered a folk theo rem that it is easy to construct field theories fulfilling either the locality or the spectrum condition. The construction of an example for the latter case is particularly easy. Take for instance an irreducible representation of the Poincare group with positive energy, and as an algebra of observables all compact operators in that representation space. This algebra of observables is even an asymptotically Abelian algebra. Since it has only a single repre sentation - except for multiples of this one - it is hardly possible to replace locality in order to obtain a theory with a reasonable physical structure. This example shows that it is not sufficient to replace locality by asymptotic Abelian-ness. The construction of a theory fulfilling locality without a pos itive energy representation was first done by Doplicher, Regge, and Singer [DRS]. However, modern investigations on the locality ideal in the algebra oftest functions, started by Alcantara and Yngvason [AY], seem to indicate that this is a general feature; this means that most of the algebras of ob servables fulfilling the locality condition will not have representations that also fulfil the spectrum condition. This discussion shows that quantum field theory becomes a subject of interest only if both conditions are satisfied at the same time.

Translation Group and Particle Representations in Quantum Field Theory

Author : Hans-Jürgen Borchers
Publisher : Springer Science & Business Media
ISBN 13 : 3540499547
Total Pages : 143 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Translation Group and Particle Representations in Quantum Field Theory by : Hans-Jürgen Borchers

Download or read book Translation Group and Particle Representations in Quantum Field Theory written by Hans-Jürgen Borchers and published by Springer Science & Business Media. This book was released on 2008-11-30 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the time I learned quantum field theory it was considered a folk theo rem that it is easy to construct field theories fulfilling either the locality or the spectrum condition. The construction of an example for the latter case is particularly easy. Take for instance an irreducible representation of the Poincare group with positive energy, and as an algebra of observables all compact operators in that representation space. This algebra of observables is even an asymptotically Abelian algebra. Since it has only a single repre sentation - except for multiples of this one - it is hardly possible to replace locality in order to obtain a theory with a reasonable physical structure. This example shows that it is not sufficient to replace locality by asymptotic Abelian-ness. The construction of a theory fulfilling locality without a pos itive energy representation was first done by Doplicher, Regge, and Singer [DRS]. However, modern investigations on the locality ideal in the algebra oftest functions, started by Alcantara and Yngvason [AY], seem to indicate that this is a general feature; this means that most of the algebras of ob servables fulfilling the locality condition will not have representations that also fulfil the spectrum condition. This discussion shows that quantum field theory becomes a subject of interest only if both conditions are satisfied at the same time.

Quantum Theory, Groups, Fields and Particles

Author : A. O. Barut
Publisher : Springer Science & Business Media
ISBN 13 : 9781402003240
Total Pages : 348 pages
Book Rating : 4.0/5 (32 download)

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Book Synopsis Quantum Theory, Groups, Fields and Particles by : A. O. Barut

Download or read book Quantum Theory, Groups, Fields and Particles written by A. O. Barut and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Symmetry and Dynamics have played, sometimes dualistic, sometimes complimentary, but always a very essential role in the physicist's description and conception of Nature. These are again the basic underlying themes of the present volume. It collects self-contained introductory contributions on some of the recent developments both in mathematical concepts and in physical applications which are becoming very important in current research. So we see in this volume, on the one hand, differential geometry, group representations, topology and algebras and on the other hand, particle equations, particle dynamics and particle interactions. Specifically, this book contains a complete exposition of the theory of deformations of symplectic algebras and quantization, expository material on topology and geometry in physics, and group representations. On the more physical side, we have studies on the concept of particles, on conformal spinors of Cartan, on gauge and supersymmetric field theories, and on relativistic theory of particle interactions and the theory of magnetic resonances. The contributions collected here were originally delivered at two Meetings in Turkey, at Blacksea University in Trabzon and at the University of Bosphorus in Istanbul. But they have been thoroughly revised, updated and extended for this volume. It is a pleasure for me to acknowledge the support of UNESCO, the support and hospitality of Blacksea and Bosphorus Universities for these two memorable Meetings in Mathematical Physics, and to thank the Contributors for their effort and care in preparing this work.

Quantum Field Theory Conformal Group Theory Conformal Field Theory

Author : R. Mirman
Publisher : iUniverse
ISBN 13 : 0595336922
Total Pages : 313 pages
Book Rating : 4.5/5 (953 download)

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Book Synopsis Quantum Field Theory Conformal Group Theory Conformal Field Theory by : R. Mirman

Download or read book Quantum Field Theory Conformal Group Theory Conformal Field Theory written by R. Mirman and published by iUniverse. This book was released on 2005-02 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conformal group is the invariance group of geometry (which is not understood), the largest one. Physical applications are implied, as discussed, including reasons for interactions. The group structure as well as those of related groups are analyzed. An inhomogeneous group is a subgroup of a homogeneous one because of nonlinearities of the realization. Conservation of baryons (protons can't decay) is explained and proven. Reasons for various realizations, so matrix elements, of the Lorentz group given. The clearly relevant mass level formula is compared with experimental values. Questions, implications and possibilities, including for differential equations, are raised.

An Introduction To Quantum Field Theory

Author : Michael E. Peskin
Publisher : CRC Press
ISBN 13 : 0429983182
Total Pages : 866 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis An Introduction To Quantum Field Theory by : Michael E. Peskin

Download or read book An Introduction To Quantum Field Theory written by Michael E. Peskin and published by CRC Press. This book was released on 2018-05-04 with total page 866 pages. Available in PDF, EPUB and Kindle. Book excerpt: An Introduction to Quantum Field Theory is a textbook intended for the graduate physics course covering relativistic quantum mechanics, quantum electrodynamics, and Feynman diagrams. The authors make these subjects accessible through carefully worked examples illustrating the technical aspects of the subject, and intuitive explanations of what is going on behind the mathematics. After presenting the basics of quantum electrodynamics, the authors discuss the theory of renormalization and its relation to statistical mechanics, and introduce the renormalization group. This discussion sets the stage for a discussion of the physical principles that underlie the fundamental interactions of elementary particle physics and their description by gauge field theories.

Quantum Field Theory

Author : Kazuhiko Nishijima
Publisher : Springer Nature
ISBN 13 : 9402421904
Total Pages : 571 pages
Book Rating : 4.4/5 (24 download)

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Book Synopsis Quantum Field Theory by : Kazuhiko Nishijima

Download or read book Quantum Field Theory written by Kazuhiko Nishijima and published by Springer Nature. This book was released on 2022-11-12 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a translation of the 8th edition of Prof. Kazuhiko Nishijima’s classical textbook on quantum field theory. It is based on the lectures the Author gave to students and researchers with diverse interests over several years in Japan. The book includes both the historical development of QFT and its practical use in theoretical and experimental particle physics, presented in a pedagogical and transparent way and, in several parts, in a unique and original manner. The Author, Academician Nishijima, is the inventor (independently from Murray Gell-Mann) of the third (besides the electric charge and isospin) quantum number in particle physics: strangeness. He is also most known for his works on several other theories describing particles such as electron and muon neutrinos, and his work on the so-called Gell-Mann–Nishijima formula. The present English translation from its 8th Japanese edition has been initiated and taken care of by the editors Prof. M. Chaichian and Dr. A. Tureanu from the University of Helsinki, who were close collaborators of Prof. Nishijima. Dr. Yuki Sato, a researcher in particle physics at the University of Nagoya, most kindly accepted to undertake the heavy task of translation. The translation of the book can be regarded as a tribute to Prof. Nishijima's memory, for his fundamental contributions to particle physics and quantum field theory. The book presents with utmost clarity and originality the most important topics and applications of QFT which by now constitute the established core of the theory. It is intended for a wide circle of graduate and post-graduate students, as well as researchers in theoretical and particle physics. In addition, the book can be a useful source as a basic material or supplementary literature for lecturers giving a course on quantum field theory.

Operational Quantum Theory II

Author : Heinrich Saller
Publisher : Springer Science & Business Media
ISBN 13 : 0387346449
Total Pages : 341 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Operational Quantum Theory II by : Heinrich Saller

Download or read book Operational Quantum Theory II written by Heinrich Saller and published by Springer Science & Business Media. This book was released on 2006-09-24 with total page 341 pages. Available in PDF, EPUB and Kindle. Book excerpt: Operational Quantum Theory II is a distinguished work on quantum theory at an advanced algebraic level. The classically oriented hierarchy with objects such as particles as the primary focus, and interactions of the objects as the secondary focus is reversed with the operational interactions as basic quantum structures. Quantum theory, specifically relativistic quantum field theory is developed the theory of Lie group and Lie algebra operations acting on both finite and infinite dimensional vector spaces. This book deals with the operational concepts of relativistic space time, the Lorentz and Poincaré group operations and their unitary representations, particularly the elementary articles. Also discussed are eigenvalues and invariants for non-compact operations in general as well as the harmonic analysis of noncompact nonabelian Lie groups and their homogeneous spaces. In addition to the operational formulation of the standard model of particle interactions, an attempt is made to understand the particle spectrum with the masses and coupling constants as the invariants and normalizations of a tangent representation structure of a an homogeneous space time model. Operational Quantum Theory II aims to understand more deeply on an operational basis what one is working with in relativistic quantum field theory, but also suggests new solutions to previously unsolved problems.

Quantum Theory, Groups and Representations

Author : Peter Woit
Publisher : Springer
ISBN 13 : 3319646125
Total Pages : 668 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Quantum Theory, Groups and Representations by : Peter Woit

Download or read book Quantum Theory, Groups and Representations written by Peter Woit and published by Springer. This book was released on 2017-11-01 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text systematically presents the basics of quantum mechanics, emphasizing the role of Lie groups, Lie algebras, and their unitary representations. The mathematical structure of the subject is brought to the fore, intentionally avoiding significant overlap with material from standard physics courses in quantum mechanics and quantum field theory. The level of presentation is attractive to mathematics students looking to learn about both quantum mechanics and representation theory, while also appealing to physics students who would like to know more about the mathematics underlying the subject. This text showcases the numerous differences between typical mathematical and physical treatments of the subject. The latter portions of the book focus on central mathematical objects that occur in the Standard Model of particle physics, underlining the deep and intimate connections between mathematics and the physical world. While an elementary physics course of some kind would be helpful to the reader, no specific background in physics is assumed, making this book accessible to students with a grounding in multivariable calculus and linear algebra. Many exercises are provided to develop the reader's understanding of and facility in quantum-theoretical concepts and calculations.

Quantum Field Theory and Topology

Author : Albert S. Schwarz
Publisher : Springer Science & Business Media
ISBN 13 : 366202943X
Total Pages : 277 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Quantum Field Theory and Topology by : Albert S. Schwarz

Download or read book Quantum Field Theory and Topology written by Albert S. Schwarz and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.

Particle Physics & Representation Theory

Author : Paul F. Kisak
Publisher : Createspace Independent Publishing Platform
ISBN 13 : 9781532971402
Total Pages : 154 pages
Book Rating : 4.9/5 (714 download)

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Book Synopsis Particle Physics & Representation Theory by : Paul F. Kisak

Download or read book Particle Physics & Representation Theory written by Paul F. Kisak and published by Createspace Independent Publishing Platform. This book was released on 2016-04-17 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is a natural connection between particle physics and representation theory, as first noted in the 1930s by Eugene Wigner. It links the properties of elementary particles to the structure of Lie groups and Lie algebras. According to this connection, the different quantum states of an elementary particle give rise to an irreducible representation of the Poincare group. Moreover, the properties of the various particles, including their spectra, can be related to representations of Lie algebras, corresponding to "approximate symmetries" of the universe. In quantum mechanics, any particular particle (with a given momentum distribution, location distribution, spin state, etc.) is written as a vector (or "ket") in a Hilbert space H. To help understand what types of particles can exist, it is important to classify the possibilities for H, and their properties. The particle is more precisely characterized by the associated projective Hilbert space PH, since two vectors that differ by a scalar factor (or in physics terminology, two "kets" that differ by a "phase factor") correspond to the same physical quantum state. Let G be the symmetry group of the universe - that is, the set of symmetries under which the laws of physics are invariant. (For example, one element of G is the simultaneous translation of all particles and fields forward in time by five seconds.) Starting with a particular particle in the state ket, and a symmetry transformation g in G, it is possible to apply the symmetry transformation to the particle to get a new state ket. For this picture to be consistent, it is necessary that PH holds a projective group representation of G. (For example, this condition guarantees that applying a symmetry transformation, then applying its inverse transformation, will restore the original quantum state.) Therefore, any given particle is associated with a unique (possibly trivial) representation of G on a projective vector space PH. (We say the particle "lies in," or "transforms as" the representation.) In many important cases, it can be shown that the particle is also (more specifically) associated with a group representation of G on the underlying (non-projective) space H.[2] Wigner's Theorem proves that it is a unitary representation, or possibly anti-unitary. So we conclude that each type of particle corresponds to a representation of G, and if we can classify the group representations of G, we will have much more information about the possibilities and properties of H, and hence what types of particles can exist. This book gives a fairly concise overview of the various mathematical group theories and their use in representing particle characteristics."

From Field Theory To Quantum Groups

Author : Bernard Jancewicz
Publisher : World Scientific
ISBN 13 : 9814499439
Total Pages : 351 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis From Field Theory To Quantum Groups by : Bernard Jancewicz

Download or read book From Field Theory To Quantum Groups written by Bernard Jancewicz and published by World Scientific. This book was released on 1996-06-20 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor Jerzy Lukierski, an outstanding specialist in the domain of quantum groups, will reach on May 21, 1995 the age of sixty. This is a birthday volume dedicated to him. It assumes the form of a collection of papers on a wide range of topics in modern research area from theoretical high energy physics to mathematical physics. Various topics of quantum groups will be treated with a special emphasis. Quantum groups is nowadays a very fashionable subject both in mathematics and high energy physics.

Quantum Field Theory

Author : Peter Breitenlohner
Publisher : Springer
ISBN 13 : 3540444823
Total Pages : 327 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Quantum Field Theory by : Peter Breitenlohner

Download or read book Quantum Field Theory written by Peter Breitenlohner and published by Springer. This book was released on 2008-01-11 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the occasion of W. Zimmermann's 70th birthday some eminent scientists gave review talks in honor of one of the great masters of quantum field theory. It was decided to write them up and publish them in this book, together with reprints of some seminal papers of the laureate. Thus, this volume deepens our understanding of anomalies, algebraic renormalization theory, axiomatic field theory and of much more while illuminating the past and present state of affairs and pointing to interesting problems for future research.

General Principles of Quantum Field Theory

Author : N.N. Bogolubov
Publisher : Springer Science & Business Media
ISBN 13 : 9780792305408
Total Pages : 720 pages
Book Rating : 4.3/5 (54 download)

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Book Synopsis General Principles of Quantum Field Theory by : N.N. Bogolubov

Download or read book General Principles of Quantum Field Theory written by N.N. Bogolubov and published by Springer Science & Business Media. This book was released on 1989-12-31 with total page 720 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction To Quantum Group And Integrable Massive Models Of Quantum Field Theory

Author : Mo-lin Ge
Publisher : World Scientific
ISBN 13 : 9814551198
Total Pages : 209 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Introduction To Quantum Group And Integrable Massive Models Of Quantum Field Theory by : Mo-lin Ge

Download or read book Introduction To Quantum Group And Integrable Massive Models Of Quantum Field Theory written by Mo-lin Ge and published by World Scientific. This book was released on 1990-09-24 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Proceedings consists of 6 lectures each from Prof L Takhtajan and Prof F Smirnov which were presented during the workshop.

Nuclear Science Abstracts

Author :
Publisher :
ISBN 13 :
Total Pages : 632 pages
Book Rating : 4.E/5 ( download)

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Book Synopsis Nuclear Science Abstracts by :

Download or read book Nuclear Science Abstracts written by and published by . This book was released on 1975 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: NSA is a comprehensive collection of international nuclear science and technology literature for the period 1948 through 1976, pre-dating the prestigious INIS database, which began in 1970. NSA existed as a printed product (Volumes 1-33) initially, created by DOE's predecessor, the U.S. Atomic Energy Commission (AEC). NSA includes citations to scientific and technical reports from the AEC, the U.S. Energy Research and Development Administration and its contractors, plus other agencies and international organizations, universities, and industrial and research organizations. References to books, conference proceedings, papers, patents, dissertations, engineering drawings, and journal articles from worldwide sources are also included. Abstracts and full text are provided if available.

Field Theory

Author : Pierre Ramond
Publisher : Routledge
ISBN 13 : 0429689012
Total Pages : 345 pages
Book Rating : 4.4/5 (296 download)

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Book Synopsis Field Theory by : Pierre Ramond

Download or read book Field Theory written by Pierre Ramond and published by Routledge. This book was released on 2020-09-29 with total page 345 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents recent advances of perturbative relativistic field theory in a pedagogical and straightforward way. For graduate students who intend to specialize in high-energy physics.

The Geometry of Dynamical Triangulations

Author : Jan Ambjorn
Publisher : Springer Science & Business Media
ISBN 13 : 3540633308
Total Pages : 207 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis The Geometry of Dynamical Triangulations by : Jan Ambjorn

Download or read book The Geometry of Dynamical Triangulations written by Jan Ambjorn and published by Springer Science & Business Media. This book was released on 1997-09-18 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book analyses in depth the geometrical aspects of the simplicial quantum gravity model known as the dynamical triangulations approach. The authors provide a compact and convenient account suitable both to introduce the non-expert reader to the spirit of the subject and to provide a well-chosen mathematical route to the heart of the matter for the expert. The techniques described in the book are novel and allow points of current interest in the subject of simplicial quantum gravity to be addressed. The authors discuss piecewise linear manifolds and give entropy estimates of the number of triangulations of 3- and 4-manifolds. Continuum physics is recovered through scaling limits and computer simulation is used to study simplicial quantum gravity extensively. The beginner will appreciate the introduction to the field and the expert the comprehensive account of recent results and developments.