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Author: Yavuz Nutku
Publisher: CRC Press
ISBN: 042998250X
Category : Science
Languages : en
Pages : 342
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Book Description
This book provides an understanding of conformal field theory and its importance to both statistical mechanics and string theory. It introduces the Wess-Zumino-Novokov-Witten (WZNW) models and their current algebras, the affine Kac-Moody algebras.
Author: Yavuz Nutku
Publisher: CRC Press
ISBN: 042998250X
Category : Science
Languages : en
Pages : 342
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Book Description
This book provides an understanding of conformal field theory and its importance to both statistical mechanics and string theory. It introduces the Wess-Zumino-Novokov-Witten (WZNW) models and their current algebras, the affine Kac-Moody algebras.
Author: Sergei V Ketov
Publisher: World Scientific
ISBN: 9814502529
Category : Science
Languages : en
Pages : 502
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Book Description
Conformal field theory is an elegant and powerful theory in the field of high energy physics and statistics. In fact, it can be said to be one of the greatest achievements in the development of this field. Presented in two dimensions, this book is designed for students who already have a basic knowledge of quantum mechanics, field theory and general relativity. The main idea used throughout the book is that conformal symmetry causes both classical and quantum integrability. Instead of concentrating on the numerous applications of the theory, the author puts forward a discussion of the general methods of conformal field theory as a physical theory. Hence the book provides in a self-contained way the necessary knowledge and “conformal” intuition which underline the various applications of conformal field theory. It is aimed to assist students and professionals in the study of the theory from its first principles and in applying the methods in their own research. The first of its kind, this book promises to give a detailed and comprehensive insight into the workings of conformal field theory.
Author: Marc Gillioz
Publisher: Springer Nature
ISBN: 303127086X
Category : Science
Languages : en
Pages : 93
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Book Description
This book is a set of introductory lecture notes on Conformal Field Theory (CFT). Unlike most existing reviews on the subject, CFT is presented here from the perspective of a unitary quantum field theory in Minkowski space-time. The book starts with a non-perturbative formulation of quantum field theory (Wightman axioms) and then, gradually, focuses on the implications of scale and special conformal symmetry, all the way to the modern conformal bootstrap. This approach includes topics such as subtleties of conformal transformations in Minkowski space-time, the construction of Wightman functions and time-ordered correlators both in position- and momentum-space, unitarity bounds derived from the spectral representation, and the appearance of UV and IR divergences. In each chapter, the reader finds useful exercises to master the subject. This book is meant for graduate students in theoretical physics and for more advanced researchers working in high-energy physics who are not necessarily familiar with the concepts of conformal field theory. Prior knowledge of quantum field theory is needed to master the arguments.
Author: Ralph Blumenhagen
Publisher: Springer
ISBN: 3642004504
Category : Science
Languages : en
Pages : 270
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Book Description
Based on class-tested notes, this text offers an introduction to Conformal Field Theory with a special emphasis on computational techniques of relevance for String Theory. It introduces Conformal Field Theory at a basic level, Kac-Moody algebras, one-loop partition functions, Superconformal Field Theories, Gepner Models and Boundary Conformal Field Theory. Eventually, the concept of orientifold constructions is explained in detail for the example of the bosonic string. In providing many detailed CFT calculations, this book is ideal for students and scientists intending to become acquainted with CFT techniques relevant for string theory but also for students and non-specialists from related fields.
Author: Ulrike Luise Tillmann
Publisher: Cambridge University Press
ISBN: 9780521540490
Category : Mathematics
Languages : en
Pages : 596
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Book Description
The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.
Author: Martin Schottenloher
Publisher: Springer Science & Business Media
ISBN: 3540706909
Category : Science
Languages : en
Pages : 153
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Book Description
Part I gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. The conformal groups are determined and the appearence of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. Part II surveys more advanced topics of conformal field theory such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface.
Author: Gerald B. Folland
Publisher: American Mathematical Soc.
ISBN: 1470464837
Category : Education
Languages : en
Pages : 342
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Book Description
Quantum field theory has been a great success for physics, but it is difficult for mathematicians to learn because it is mathematically incomplete. Folland, who is a mathematician, has spent considerable time digesting the physical theory and sorting out the mathematical issues in it. Fortunately for mathematicians, Folland is a gifted expositor. The purpose of this book is to present the elements of quantum field theory, with the goal of understanding the behavior of elementary particles rather than building formal mathematical structures, in a form that will be comprehensible to mathematicians. Rigorous definitions and arguments are presented as far as they are available, but the text proceeds on a more informal level when necessary, with due care in identifying the difficulties. The book begins with a review of classical physics and quantum mechanics, then proceeds through the construction of free quantum fields to the perturbation-theoretic development of interacting field theory and renormalization theory, with emphasis on quantum electrodynamics. The final two chapters present the functional integral approach and the elements of gauge field theory, including the Salam–Weinberg model of electromagnetic and weak interactions.
Author: Ioannis John Demetrius Vergados
Publisher: World Scientific Publishing Company
ISBN: 9813202467
Category : Science
Languages : en
Pages : 349
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Book Description
This volume goes beyond the understanding of symmetries and exploits them in the study of the behavior of both classical and quantum physical systems. Thus it is important to study the symmetries described by continuous (Lie) groups of transformations. We then discuss how we get operators that form a Lie algebra. Of particular interest to physics is the representation of the elements of the algebra and the group in terms of matrices and, in particular, the irreducible representations. These representations can be identified with physical observables.This leads to the study of the classical Lie algebras, associated with unitary, unimodular, orthogonal and symplectic transformations. We also discuss some special algebras in some detail. The discussion proceeds along the lines of the Cartan-Weyl theory via the root vectors and root diagrams and, in particular, the Dynkin representation of the roots. Thus the representations are expressed in terms of weights, which are generated by the application of the elements of the algebra on uniquely specified highest weight states. Alternatively these representations can be described in terms of tensors labeled by the Young tableaux associated with the discrete symmetry Sn. The connection between the Young tableaux and the Dynkin weights is also discussed. It is also shown that in many physical systems the quantum numbers needed to specify the physical states involve not only the highest symmetry but also a number of sub-symmetries contained in them. This leads to the study of the role of subalgebras and in particular the possible maximal subalgebras. In many applications the physical system can be considered as composed of subsystems obeying a given symmetry. In such cases the reduction of the Kronecker product of irreducible representations of classical and special algebras becomes relevant and is discussed in some detail. The method of obtaining the relevant Clebsch-Gordan (C-G) coefficients for such algebras is discussed and some relevant algorithms are provided. In some simple cases suitable numerical tables of C-G are also included.The above exposition contains many examples, both as illustrations of the main ideas as well as well motivated applications. To this end two appendices of 51 pages — 11 tables in Appendix A, summarizing the material discussed in the main text and 39 tables in Appendix B containing results of more sophisticated examples are supplied. Reference to the tables is given in the main text and a guide to the appropriate section of the main text is given in the tables.
Author: Yitzhak Frishman
Publisher: Cambridge University Press
ISBN: 1139486489
Category : Science
Languages : en
Pages : 455
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Book Description
Providing a new perspective on quantum field theory, this book is useful for graduate students and researchers within and outside the field. It describes non-perturbative methods, and explores two-dimensional and four-dimensional gauge dynamics using those methods. Applications are thoroughly described.
Author: Brian Hatfield
Publisher: CRC Press
ISBN: 0429972865
Category : Science
Languages : en
Pages : 474
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Book Description
First Published in 2018. The emphasis of the book is calculational, and most computations are presented in step-by-step detail. The book is unique in that it develops all three representations of quantum field theory (operator, functional Schr dinger, and path integral) for point particles and strings. In many cases, identical results are worked out in each representation to emphasize the representation-independent structures of quantum field theory
