Fiorenzo Bastianelli / Universita degli Studi, Bologna, Italy
Peter van Nieuwenhuizen / State University of New York

Path Integrals and Anomalies in Curved Space

Series: Cambridge Monographs on Mathematical Physics
Hardback (ISBN-10: 0521847613 | ISBN-13: 9780521847612)

Path integrals provide a powerful method for describing quantum phenomena. This book introduces the quantum mechanics of particles that move in curved space by employing path integrals and then using them to compute anomalies in quantum field theories. The authors start by deriving path integrals for particles moving in curved space and their supersymmetric generalizations. They then discuss the regularization schemes essential to constructing and computing these path integrals. This topic is used to introduce regularization and renormalization in quantum field theories in a wider context. These methods are then applied to discuss and calculate anomalies in quantum field theory. Such anomalies provide enormous constraints in the search for physical theories of elementary particles, quantum gravity and string theories. An advanced text for researchers and graduate students of quantum field theory and string theory, the first part is also a stand-alone introduction to path integrals in quantum mechanics.

* Contains very detailed and complete derivations of path integrals in curved space, both for bosonic and fermionic point particles

* Provides a model to study regularization and renormalization issues

* Extensive calculations of anomalies in curved spaces and in particular, gravitational anomalies

Contents

Part I. Path Integrals for Quantum Mechanics in Curved Space: 1. Introduction to path integrals; 2. Time slicing; 3. Mode regularization; 4. Dimensional regularization; Part II. Applications to Anomalies: 5. Introduction to anomalies; 6. Chiral anomalies from SUSY quantum fields; 7. Trace anomalies from ordinary and SUSY quantum mechanics; 8. Conclusions and summary.

Herbert Edelsbrunner / Duke University, North Carolina

Geometry and Topology for Mesh Generation

Series: Cambridge Monographs on Applied and Computational Mathematics (No. 7)
Paperback (ISBN-10: 052168207X | ISBN-13: 9780521682077)


The book combines topics in mathematics (geometry and topology), computer science (algorithms), and engineering (mesh generation). The motivation for these topics is the difficulty, both conceptually and in the technical execution, of combining elements of combinatorial and of numerical algorithms. Mesh generation is a topic where a meaningful combination of these different approaches to problem solving is inevitable. The book develops methods from both areas that are amenable to combination, and explains recent breakthrough solutions to meshing that fit into this category. This book emphasizes topics that are elementary, attractive, useful, interesting, and lend themselves to teaching, making it an ideal graduate text for courses on mesh generation.

* Combines topics from mathematics, computer science, and engineering

* Based upon a graduate-level course given at Duke University

* Has wide application in both industry and academia

Contents

1. Delaunay triangulations; 2. Triangle meshes; 3. Combinatorial topology; 4. Surface simplification; 5. Delaunay tetrahedrizations; 6. Tetrahedron meshes; 7. Open problems.

Reviews

‘The book is an ideal graduate text for courses on mesh generation. The topics of the books are elementary, attractive, useful, interesting, and one section deals with open question in this area.’ Mathematical Reviews

‘… a very readable exposition …’. Monatshefte fur Mathematik

‘… well organised … We recommend the book to graduate students and researchers in computational geometry.’ Janos Kincses, Acta Sci. Math.

K. F. Riley / M. P. Hobson

Student Solution Manual for Mathematical Methods for Physics and Engineering, Third Edition

Paperback (ISBN-10: 0521679737 | ISBN-13: 9780521679732)

Mathematical Methods for Physics and Engineering, Third Edition is a highly acclaimed undergraduate textbook that teaches all the mathematics for an undergraduate course in any of the physical sciences. As well as lucid descriptions of all the topics and many worked examples, it contains over 800 exercises. New stand-alone chapters give a systematic account of the 'special functions' of physical science, cover an extended range of practical applications of complex variables, and give an introduction to quantum operators. This solutions manual accompanies the third edition of Mathematical Methods for Physics and Engineering. It contains complete worked solutions to over 400 exercises in the main textbook, the odd-numbered exercises, that are provided with hints and answers. The even-numbered exercises have no hints, answers or worked solutions and are intended for unaided homework problems; full solutions are available to instructors on a password-protected web site, www.cambridge.org/9780521679718.

* Complete and fully-worked solutions to over 400 problems from the textbook

* Detailed and clear presentation, with the original questions reproduced in full

* Remainder of exercises can be set for unaided homework, worked solutions are available to lecturers

Contents

Preface; 1. Preliminary algebra; 2. Preliminary calculus; 3. Complex numbers and hyperbolic functions; 4. Series and limits; 5. Partial differentiation; 6. Multiple integrals; 7. Vector algebra; 8. Matrices and vector spaces; 9. Normal modes; 10. Vector calculus; 11. Line, surface and volume integrals; 12. Fourier series; 13. Integral transforms; 14. First-order ordinary differential equations; 15. Higher-order ordinary differential equations; 16. Series solutions of ordinary differential equations; 17. Eigenfunction methods for differential equations; 18. Special functions; 19. Quantum operators; 20. Partial differential equations: general and particular; 21. Partial differential equations: separation of variables; 22. Calculus of variations; 23. Integral equations; 24. Complex variables; 25. Application of complex variables; 26. Tensors; 27. Numerical methods; 28. Group theory; 29. Representation theory; 30. Probability; 31. Statistics.

Ron Roth / Technion - Israel Institute of Technology, Haifa

Introduction to Coding Theory

Hardback (ISBN-10: 0521845041 | ISBN-13: 9780521845045)

Courses: (Introduction to) Coding Theory Error-Correcting Codes
Levels: GRADUATE

Error-correcting codes constitute one of the key ingredients in achieving the high degree of reliability required in modern data transmission and storage systems. This book introduces the reader to the theoretical foundations of error-correcting codes, with an emphasis on Reed-Solomon codes and their derivative codes. After reviewing linear codes and finite fields, the author describes Reed-Solomon codes and various decoding algorithms. Cyclic codes are presented, as are MDS codes, graph codes, and codes in the Lee metric. Concatenated, trellis, and convolutional codes are also discussed in detail. Homework exercises introduce additional concepts such as Reed-Muller codes, and burst error correction. The end-of-chapter notes often deal with algorithmic issues, such as the time complexity of computational problems. While mathematical rigor is maintained, the text is designed to be accessible to a broad readership, including students of computer science, electrical engineering, and mathematics, from senior-undergraduate to graduate level.

* Contains classical introductory material and classical research material as well as more recent developments

* Accessible to computer scientists, electrical engineers and mathematicians

* Contains over 340 exercises (many with hints) and over 100 worked examples

Contents

Preface; 1. Introduction; 2. Linear codes; 3. Introduction to finite fields; 4. Bounds on the parameters of codes; 5. Reed-Solomon codes and related codes; 6. Decoding of Reed-Solomon codes; 7. Structure of finite fields; 8. Cyclic codes; 9. List decoding of Reed-Solomon codes; 10. Codes in the Lee metric; 11. MDS codes; 12. Concatenated codes; 13. Graph codes; 14. Trellis codes and convolutional codes; Appendix A. Basics in modern algebra; Bibliography; List of symbols; Index.

Review

'… a most welcome addition. … well tested as a course text. Features include, the extensive collections of interesting and nontrivial problems at the end of chapters, the clear and insightful explanations of some of the deeper aspects of the subject and the extensive, interesting and useful historical notes on the development of the subject. This is an excellent volume that will reward the participants in any course that uses it with a deep understanding and appreciation for the subject.' Ian F, Blake, Department of Electrical and Computer Engineering, University of Toronto, Canada

Tamas Tel / Lorand Eotvos University, Budapest
Marton Gruiz / Lorand Eotvos University, Budapest

Chaotic Dynamics

Hardback (ISBN-10: 0521839122 | ISBN-13: 9780521839129)
Paperback (ISBN-10: 0521547830 | ISBN-13: 9780521547839)

Lecturers can request inspection copies of this title.
Courses: Chaotic Dynamics, Dynamical Systems, Chaos, Nonlinear Dynamics
Levels: 2ND OR 3RD YEAR U/G; 1ST YEAR G
In the past few decades we have come to understand that even motions in simple systems can have complex and surprising properties. Chaotic Dynamics provides a clear introduction to these chaotic phenomena, based on geometrical interpretations and simple arguments, without the need for prior in-depth scientific and mathematical knowledge. Richly illustrated throughout, examples are taken from classical mechanics whose elementary laws are familiar to the reader. In order to emphasize the general features of chaos, the most important relations are also given in simple mathematical forms, independent of any mechanical interpretation. A broad range of potential applications are presented, ranging from everyday phenomena through engineering and environmental problems to astronomical aspects. Chaos occurs in a variety of scientific disciplines, and proves to be the rule, not the exception. This book is primarily intended for undergraduate students in science, engineering, and mathematics.

* Clear pedagogical presentation, rich in illustrations, that provides a broad coverage of aspects of chaos

* Presents important features of chaotic phenomena within a framework of classical mechanics

* Includes many worked examples as well as problems with half of the solutions available to lecturers from solutions@cambridge.org

Contents

Introduction; Part I. The Phenomenon: Complex Motion, Unusual Geometry: 1. Chaotic motions; 2. Fractal objects; Part II. Preparatory Concepts: 3. Regular motions; 4. Driven motions; Part III. Investigation of Chaotic Motion: 5. Chaos in dissipative systems; 6. Transient chaos in dissipative systems; 7. Chaos in conservative systems; 8. Chaotic scattering; 9. Applications of chaos; 10. Epilogue, outlook; Part IV. Miscellaneous: 11. Appendices; 12. Solutions to problems; 13. Bibliography