Hardback (ISBN-13: 9780521850827)
20 line diagrams 5 half-tones 80 exercises
Page extent: 330 pages
Size: 247 x 174 mm
Presenting a variety of topics that are only briefly touched on in other texts, this book provides a thorough introduction to the techniques of field theory. Covering Feynman diagrams and path integrals, the author emphasizes the path integral approach, the Wilsonian approach to renormalization, and the physics of non-abelian gauge theory. It provides a thorough treatment of quark confinement and chiral symmetry breaking, topics not usually covered in other texts at this level. The Standard Model of particle physics is discussed in detail. Connections with condensed matter physics are explored, and there is a brief, but detailed, treatment of non-perturbative semi-classical methods. Ideal for graduate students in high energy physics and condensed matter physics, the book contains many problems,which help students practise the key techniques of quantum field theory.
* Contains a thorough treatment of quark confinement and chiral symmetry
breaking - important topics not covered in many introductory texts * Includes
the Wilsonian approach to renormalization and effective field theory, providing
a conceptual understanding of this crucial part of the subject * Enables
students to gain hands-on acquaintance with the key techniques of QFT through
problem sets
Contents
1. Introduction; 2. Quantum theory of free scalar fields; 3. Interacting field theory; 4. Particles of spin one, and gauge invariance; 5. Spin 1/2 particles and Fermi statistics; 6. Massive quantum electrodynamics; 7. Symmetries, Ward identities and Nambu Goldstone bosons; 8. Non-abelian gauge theory; 9. Renormalization and effective field theory; 10. Instantons and solitons; 11. Concluding remarks; Appendices; References; Index.
Hardback (ISBN-13: 9780521895934)
35 line diagrams
Page extent: 296 pages
Size: 247 x 174 mm
While statistical mechanics describe the equilibrium state of systems with many degrees of freedom, and dynamical systems explain the irregular evolution of systems with few degrees of freedom, new tools are needed to study the evolution of systems with many degrees of freedom. This book presents the basic aspects of chaotic systems, with emphasis on systems composed by huge numbers of particles. Firstly, the basic concepts of chaotic dynamics are introduced, moving on to explore the role of ergodicity and chaos for the validity of statistical laws, and ending with problems characterized by the presence of more than one significant scale. Also discussed is the relevance of many degrees of freedom, coarse graining procedure, and instability mechanisms in justifying a statistical description of macroscopic bodies. Introducing the tools to characterize the non asymptotic behaviors of chaotic systems, this text will interest researchers and graduate students in statistical mechanics and chaos.
* Introduces the tools necessary to characterise the non-asymptotic behaviours
of chaotic systems * Discusses the role of coarse graining and many degrees
of freedom in statistical physics * Presents and analyses some models (e.g.
Fermi-Pasta-Ulam, the piston, high dimensional symplectic maps) with advanced
tools such as Finite-scale - Lyapunov-exponents, epsilon entropy and multiscale
techniques
Contents
1. Basic concepts of dynamical systems theory; 2. Dynamical indicators for chaotic systems: Lyapunov exponents, entropies and beyond; 3. Coarse graining, entropies and Lyapunov exponents at work; 4. Foundation of the statistical mechanics and dynamical systems; 5. On the origin of irreversibility; 6. The role of chaos in non-equilibrium statistical mechanics; 7. Coarse-graining equations in complex systems; 8. Renormalization-group approaches; Index.
Series: Cambridge Tracts in Mathematics (No. 123)
Paperback (ISBN-13: 9780521055192)
Page extent: 379 pages
Size: 228 x 152 mm
Weight: 0.576 kg
The ends of a topological space are the directions in which it becomes non-compact by tending to infinity. The tame ends of manifolds are particularly interesting, both for their own sake, and for their use in the classification of high-dimensional compact manifolds. The book is devoted to the related theory and practice of ends, dealing with manifolds and CW complexes in topology and chain complexes in algebra. The first part develops a homotopy model of the behaviour at infinity of a non-compact space. The second part studies tame ends in topology. Tame ends are shown to have a uniform structure, with a periodic shift map. Approximate fibrations are used to prove that tame manifold ends are the infinite cyclic covers of compact manifolds. The third part translates these topological considerations into an appropriate algebraic context, relating tameness to homological properties and algebraic K- and L-theory.
* Ranicki is a well-known author * This book ties up all the loose ends
of the subject * Features a blend of geometric topology, algebraic topology
and algebra, designed to appeal to readers with background in only one
of these disciplines
Contents
Introduction; Chapter summaries; Part I. Topology at Infinity: 1. End spaces; 2. Limits; 3. Homology at infinity; 4. Cellular homology; 5. Homology of covers; 6. Projective class and torsion; 7. Forward tameness; 8. Reverse tameness; 9. Homotopy at infinity; 10. Projective class at infinity; 11. Infinite torsion; 12. Forward tameness is a homotopy pushout; Part II. Topology Over the Real Line: 13. Infinite cyclic covers; 14. The mapping torus; 15. Geometric ribbons and bands; 16. Approximate fibrations; 17. Geometric wrapping up; 18. Geometric relaxation; 19. Homotopy theoretic twist glueing; 20. Homotopy theoretic wrapping up and relaxation; Part III. The Algebraic Theory: 21. Polynomial extensions; 22. Algebraic bands; 23. Algebraic tameness; 24. Relaxation techniques; 25. Algebraic ribbons; 26. Algebraic twist glueing; 27. Wrapping up in algebraic K- and L-theory; Part IV. Appendices; References; Index.
Zurich Lectures in Advanced Mathematics
ISBN 978-3-03719-044-9
February 2008, 134 pages, softcover, 17.0 cm x 24.0 cm.
The characterization of rectifiable sets through the existence of densities is a pearl of geometric measure theory. The difficult proof, due to Preiss, relies on many beautiful and deep ideas and novel techniques. Some of them have already proven useful in other contexts, whereas others have not yet been exploited. These notes give a simple and short presentation of the former, and provide some perspective of the latter.
This text emerged from a course on rectifiability given at the University of Zurich. It is addressed both to researchers and students, the only prerequisite is a solid knowledge in standard measure theory. The first four chapters give an introduction to rectifiable sets and measures in euclidean spaces, covering classical topics such as the area formula, the theorem of Marstrand and the most elementary rectifiability criterions. The fifth chapter is dedicated to a subtle rectifiability criterion due to Marstrand and generalized by Mattila, and the last three focus on Preiss' result. The aim is to provide a self-contained reference for anyone interested in an overview of this fascinating topic.
Table of contents
EMS Textbooks in Mathematics
ISBN 978-3-03719-043-2
February 2008, 427 pages, hardcover, 16.5 cm x 23.5 cm.
This book provides an introduction to the theory of quantum groups with emphasis on their duality and on the setting of operator algebras.
Part I of the text presents the basic theory of Hopf algebras, Van Daele’s
duality theory of algebraic quantum groups, and Woronowicz’s compact quantum
groups, staying in a purely algebraic setting. Part II focuses on quantum
groups in the setting of operator algebras. Woronowicz’s compact quantum
groups are treated in the setting of C*-algebras, and the fundamental multiplicative
unitaries of Baaj and Skandalis are studied in detail. An outline of Kustermans’
and Vaes’ comprehensive theory of locally compact quantum groups completes
this part. Part III leads to selected topics, such as coactions, Baaj*Skandalis-duality,
and approaches to quantum groupoids in the setting of operator algebras.
The book is addressed to graduate students and non-experts from other fields. Only basic knowledge of (multi-) linear algebra is required for the first part, while the second and third part assume some familiarity with Hilbert spaces, C*-algebras, and von Neumann algebras.
Table of contents
EMS Textbooks in Mathematics
ISBN 978-3-03719-041-8
March 2008, 187 pages, hardcover, 16.5 cm x 23.5 cm.
This book quickly introduces beginners to general group theory and then focuses on three main themes:
finite group theory, including sporadic groups;
combinatorial and geometric group theory, including the Bass*Serre theory
of groups acting on trees;
the theory of train tracks by Bestvina and Handel for automorphisms of free groups.
With its many examples, exercises, and full solutions to selected exercises, this text provides a gentle introduction that is ideal for self-study and an excellent preparation for applications. A distinguished feature of the presentation is that algebraic and geometric techniques are balanced. The beautiful
theory of train tracks is illustrated by two nontrivial examples.
Presupposing only a basic knowledge of algebra, the book is addressed to anyone interested in group theory: from advanced undergraduate and graduate students to specialists.
Table of contents
EMS Textbooks in Mathematics
ISBN 978-3-03719-049-4
March 2008, 367 pages, hardcover, 16.5 cm x 23.5 cm.
This book provides a comprehensive introduction to the field of several complex variables in the setting of a very special but basic class of domains, the so-called Reinhardt domains. In this way the reader may learn much about this area without encountering too many technical difficulties.
Chapter 1 describes the fundamental notions and the phenomenon of simultaneous holomorphic extension. Chapter 2 presents a fairly complete discussion of biholomorphisms of bounded (complete) Reinhardt domains in the two dimensional case. The third chapter gives a classification of Reinhardt domains of existence for the most important classes of holomorphic functions. The last chapter deals with invariant functions and gives explicit calculations of many of them on certain Reinhardt domains. Numerous exercises are included to help the readers with their understanding of the material. Further results and open problems are added which may be useful as seminar topics.
The primary aim of this book is to introduce students or non-experts to some of the main research areas in several complex variables. The book provides a friendly invitation to this field as the only prerequisite is a basic knowledge of analysis.
Table of contents