March 2004 | Hardback | 505 pages 76 line
diagrams 7 tables |
ISBN: 0-521-83836-3
Topological solitons occur in many nonlinear
classical field
theories. They are stable, particle-like
objects, with finite
mass and a smooth structure. Examples are
monopoles and
Skyrmions, Ginzburg?Landau vortices and sigma-model
lumps, and
Yang?Mills instantons. This book is a comprehensive
survey of
static topological solitons and their dynamical
interactions.
Particular emphasis is placed on the solitons
which satisfy first-order
Bogomolny equations. For these, the soliton
dynamics can be
investigated by finding the geodesics on
the moduli space of
static multi-soliton solutions. Remarkable
scattering processes
can be understood this way. The book starts
with an introduction
to classical field theory, and a survey of
several mathematical
techniques useful for understanding many
types of topological
soliton. Subsequent chapters explore key
examples of solitons in
one, two, three and four dimensions. The
final chapter discusses
the unstable sphaleron solutions which exist
in several field
theories.
Contents
Preface; 1. Introduction; 2. Lagrangians
and fields; 3. Topology
in field theory; 4. Solitons: general theory;
5. Kinks; 6. Lumps
and rational maps; 7. Vortices; 8. Monopoles;
9. Skyrmions; 10.
Instantons; 11. Saddle points: sphalerons;
References; Index.
May 2004 | Hardback | 550 pages 105 line
diagrams 8 tables 156
exercises | ISBN: 0-521-83143-1
An accessible introduction to string theory,
this book provides a
detailed and self-contained demonstration
of the main concepts
involved. The first part deals with basic
ideas, reviewing
special relativity and electromagnetism while
introducing the
concept of extra dimensions. D-branes and
the classical dynamics
of relativistic strings are discussed next,
and the quantization
of open and closed bosonic strings in the
light-cone gauge, along
with a brief introduction to superstrings.
The second part begins
with a detailed study of D-branes followed
by string
thermodynamics. It discusses possible physical
applications, and
covers T-duality of open and closed strings,
electromagnetic
fields on D-branes, Born?Infeld electrodynamics,
covariant string
quantization and string interactions. Primarily
aimed as a
textbook for advanced undergraduate and beginning
graduate
courses, it will also be ideal for a wide
range of scientists and
mathematicians who are curious about string
theory.
Contents
Part I. Basics: 1. A brief introduction;
2. Special relativity
and extra dimensions; 3. Electromagnetism
and gravitation; 4. Non-relativistic
strings; 5. The relativistic point particle;
6. Relativistic
strings; 7. String parameterization and motion;
8. World-sheet
currents; 9. Light-cone relativistic strings;
10. Light-cone
fields and particles; 11. Relativistic quantum
particles; 12.
Quantum open strings; 13. Quantum closed
strings; Part II.
Developments: 14. D-branes and gauge fields;
15. String charge,
electric charge, and particle physics; 16.
String thermodynamics
and black holes; 17. T-duality of closed
strings; 18. T-duality
of open strings; 19. Electromagnetic fields
on D-branes; 20.
Nonlinear electrodynamics; 21. Covariant
string quantization; 22.
Interactions and Riemann surfaces; 23. Loop
amplitudes in string
theory; References; Index.
June 2004 | Hardback | 275 pages | ISBN:
0-521-82329-3
This book gives an overview of the classification
of the real
numbers by their approximation properties
by algebraic numbers.
The author has written for a wide audience
and made the book as
accessible and self-contained as possible.
Readers are introduced
to the subject and then lead up to some celebrated
advanced
results such as the proof of Mahler’s conjecture
on S-numbers,
the existence of T-numbers, and the theorem
of Jarnik and
Besicovitch. As such this is ideal for graduate
students or
researchers entering this field of research.
Further, the wide
bibliography (around 600 references) makes
this book very useful
for specialists.
Contents
1. Approximation by rational numbers; 2.
Approximation to
algebraic numbers; 3. The classifications
of Mahler and Koksma; 4.
Mahler's conjecture on S-numbers; 5. Hausdorff
dimension of
exceptional sets; 6. Deeper results on the
measure of exceptional
sets; 7. On T-numbers and U-numbers; 8. Other
classifications of
real and complex numbers; 9. Approximation
in other fields; 10.
Conjectures and open questions; Appendix
A. Lemmas on
polynomials; Appendix B. Geometry of numbers.
June 2004 | Paperback | 300 pages | ISBN:
0-521-54766-0
June 2004 | Hardback | 300 pages | ISBN:
0-521-83896-7
One-dimensional dynamics owns many deep results
and avenues of
active mathematical research. Numerous inroads
to this research
exist for the advanced undergraduate or beginning
graduate
student. This book provides glimpses into
one-dimensional
dynamics with the hope that the results presented
illuminate the
beauty and excitement of the field. Much
of this material is
covered nowhere else in ‘text book format’,
some are mini new
research topics in themselves, and novel
connections are drawn
with other research areas both inside and
outside the text. The
material presented here is not meant to be
approached in a linear
fashion. Readers are encouraged to pick and
choose topics of
interest. Anyone with an interest in dynamics,
novice or expert
alike, will find many topics of interest
within.
Contents
1. Topological Roots; 2. Measure Theoretic
Roots; 3. Symbolic
& Topological Dynamics; 4. Beginning
Measurable Dynamics; 5.
2? Map; 6. Kneading Maps; 7. Some Number
Theory; 8. Circle Maps;
9. Topological Entropy; 10. Symmetric Tent
Maps; 11. Adding
Machines & Maps; 12. Beta-Transformations
and Maps; 13.
Homeomorphic Restrictions; 14. Complex Quadratic
Dynamics.
Description
Translated from the second Russian edition
and with added notes
by K.A. Hirsch. Teoriya Grupp by Kurosh was
widely acclaimed, in
its first edition, as the first modern text
on the general theory
of groups, with the major emphasis on infinite
groups. The decade
that followed brought about a remarkable
growth and maturity in
the theory of groups, so that this second
edition, in English
translation, represents a complete rewriting
of the first edition.
The book can be used as a beginning text,
the only requirement
being some mathematical maturity and a knowledge
of the elements
of transfinite numbers.
Many new sections were added to this second
edition, and many old
ones were completely revised: The theory
of abelian groups was
significantly revised; many significant additions
were made to
the section on the theory of free groups
and free products; an
entire chapter is devoted to group extensions;
and the deep
changes in the theory of solvable and nilpotent
groups--one of
the large and rich branches of the theory
of groups--are covered
in this work. Each volume concludes with
Editor's Notes and a
Bibliography.
Contents
Part Three. Group-Theoretical Constructions
Free Products and Free Groups: 9.33 Definition
of a free product;
9.34 Subgroups of a free product; 9.35 Isomorphism
of free
decompositions. Free products with an amalgamated
subgroup; 9.36
Subgroups of free groups; 9.37 Fully invariant
subgroups of free
groups. Identical relations
Finitely Generated Groups: 10.38 General
properties of finitely
generated groups; 10.39 Grusko's theorem;
10.40 Grusko's theorem
(conclusion); 10.41 Groups with a finite
number of defining
relations
Direct Products. Lattices: 11.42 Preliminary
remarks; 11.43
Lattices; 11.44 Modular and complete modular
lattices; 11.45
Direct sums in complete modular lattices;
11.46 Further lemmas;
11.47 The fundamental theorem
Extensions of Groups: 12.48 Factor systems;
12.49 Extensions of
abelian groups. Cohomology groups; 12.50
Calculation of the
second cohomology group; 12.51 Extensions
of non-commutative
groups; 12.52 Special cases
Part Four. Solvable and Nilpotent Groups
Finiteness Conditions, Sylow Subgroups, and
Related Problems: 13.53
Finiteness conditions; 13.54 Sylow subgroups.
The centers of $p$-groups;
13.55 Local properties; 13.56 Normal and
invariant systems
Solvable Groups: 14.57 Solvable and generalized
solvable groups;
14.58 Local theorems. Locally solvable groups;
14.59 Solvable
groups with finiteness conditions; 14.60
Sylow $\Pi$-subgroups of
solvable groups; 14.61 Finite semi-simple
groups
Nilpotent Groups: 15.62 Nilpotent and finite
nilpotent groups; 15.63
Generalized nilpotent groups; 15.64 Connections
with solvable
groups. $S$-groups. Finiteness conditions;
15.65 Complete
nilpotent groups; 15.66 Groups with unique
extraction of roots;
15.67 Locally nilpotent torsion-free groups
Appendixes
Bibliography
Author Index
Subject Index
Details:
Series: AMS Chelsea Publishing
Publication Year: 1956
Reprint/Revision History: reprinted 1960;
first AMS printing 2003
ISBN: 0-8218-3477-0
Paging: 308 pp.
Binding: Hardcover