Part of Cambridge Monographs on Mathematical Physics
Publication planned for: June 2016
availability: Not yet published - available from June 2016
format: Hardback
isbn: 9780521768566
The possibility that we live in a higher-dimensional world with spatial dimensions greater than three started with the early work of Kaluza and Klein. However, in addressing experimental constraints, early model-builders were forced to compactify these extra dimensions to very tiny scales. With the development of brane-world scenarios it became possible to consider novel compactifications which allow the extra dimensions to be large or to provide observable effects of these dimensions at experimentally accessible energy scales. This book provides a comprehensive account of these recent developments, keeping the high-energy physics implications in focus. After an historical survey of the idea of extra dimensions, the book deals in detail with models of large extra dimensions, warped extra dimensions and other models such as universal extra dimensions. The theoretical and phenomenological implications are discussed in a pedagogical manner for both researchers and graduate students.
The first proper account of brane-world motivated models of extra dimensions and their implications for particle physics
Brings a student or working researcher up to date with the current understanding of the subject
Uses a pedagogical approach to address theoretical issues in high-energy physics and their connections to high-energy experiments
Preface
1. Dimensional dreams
2. The Standard Model and beyond
3. The birth of compact dimensions
4. String theory: a review
5. Effective theories
6. Large extra dimensions
7. Visible towers of invisible gravitons
8. Making black holes
9. Universal extra dimensions
10. Warped compactifications
11. Graviton resonances
12. Stability of warped Worlds
13. Exploring the bulk
14. Epilogue
Appendix A. General relativity in a nutshell
Appendix B. Testing the inverse square law
Index.
Series:De Gruyter Studies in Mathematics 18
Due to the strong appeal and wide use of this monograph, it is now available in
its third revised edition. The monograph gives a systematic treatment of 3-
dimensional topological quantum field theories (TQFTs) based on the work of
the author with N. Reshetikhin and O. Viro. This subject was inspired by the
discovery of the Jones polynomial of knots and the Witten-Chern-Simons field
theory. On the algebraic side, the study of 3-dimensional TQFTs has been
influenced by the theory of braided categories and the theory of quantum groups.
The book is divided into three parts. Part I presents a construction of 3-
dimensional TQFTs and 2-dimensional modular functors from so-called
modular categories. This gives a vast class of knot invariants and 3-manifold
invariants as well as a class of linear representations of the mapping class groups
of surfaces. In Part II the technique of 6j-symbols is used to define state sum
invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is
established via the theory of shadows. Part III provides constructions of modular
categories, based on quantum groups and skein modules of tangles in the 3-
space.
This fundamental contribution to topological quantum field theory is accessible
to graduate students in mathematics and physics with knowledge of basic
algebra and topology. It is an indispensable source for everyone who wishes to
enter the forefront of this fascinating area at the borderline of mathematics and physics.
* Invariants of graphs in Euclidean 3-space and of closed 3-manifolds
* Foundations of topological quantum field theory
* Three-dimensional topological quantum field theory
* Two-dimensional modular functors
* 6j-symbols
* Simplicial state sums on 3-manifolds
De Gruyter Studies in Mathematics 18
xii, 595 pages
Hardcover:
ISBN 978-3-11-044266-3
This book is an introduction to financial mathematics. It is intended for graduate
students in mathematics and for researchers working in academia and industry.
The focus on stochastic models in discrete time has two immediate benefits.
First, the probabilistic machinery is simpler, and one can discuss right away
some of the key problems in the theory of pricing and hedging of financial
derivatives. Second, the paradigm of a complete financial market, where all
derivatives admit a perfect hedge, becomes the exception rather than the rule.
Thus, the need to confront the intrinsic risks arising from market incomleteness
appears at a very early stage.
The first part of the book contains a study of a simple one-period model, which
also serves as a building block for later developments. Topics include the
characterization of arbitrage-free markets, preferences on asset profiles, an
introduction to equilibrium analysis, and monetary measures of financial risk.
In the second part, the idea of dynamic hedging of contingent claims is
developed in a multiperiod framework. Topics include martingale measures,
pricing formulas for derivatives, American options, superhedging, and hedging
strategies with minimal shortfall risk.
This fourth, newly revised edition contains more than one hundred exercises. It
also includes material on risk measures and the related issue of model
uncertainty, in particular a chapter on dynamic risk measures and sections on
robust utility maximization and on efficient hedging with convex risk measures.
* 4th revised edition.
* Includes exercises and tips for solutions.
* Suitable for students, researchers and practitioners
.
Hans Follmer, Humboldt-Universitat zu Berlin, Germany; Alexander Schied,
University of Mannheim, Germany.
De Gruyter Textbook
xii, 550 pages, 15 Figures (bw)
Paperback:
ISBN 978-3-11-046344-6
Tensor calculus is a prerequisite for many tasks in engineering and physics. By
focusing on algorithms in the coordinate representation of tensors, this graduate
textbook offers easy access to techniques in the field. It imparts the required
algebraic aids and contains numerous exercises with answers, making it suitable
for tought courses and self study for students and researchers in areas such as
fluid dynamics, solid mechanics, and electrodynamics.
While a variety of textbooks on mathematical aspects of tensor calculus are
available, this book focuses on the practical aspects allowing engineers to
directly apply the methods learned in three dimensions. By using carefully
chosen language an emphasis lies on conveying symbolic and index notation in
parallel, thus allowing for immediate applications e.g. in continuum mechanics,
electrodynamics, or signal processing. Students with basic knowledge in linear
algebra will get an understanding of the methods on an algorithmic level, rather
than by means of visualization and metaphors which are hard to apply to
practical problems.
* All methods are demonstrated in three dimensions and in coordinate form.
* A focus is placed on calculation procedures.
* Discretisation of tensor operators for numerical methods is discussed.
* Contains a variety of problems and detailed solutions.
Heinz Schade, TU Berlin.
Klaus Neemann, FH Kaiserslautern.
Andrea Dziubek and Edmond Rusjan, State Univ. of New York (SUNYIT),USA.
De Gruyter Textbook
xviii, 470 pages, 30 Figures (bw)
Paperback:
ISBN 978-3-11-040425-8
EMS Textbooks in Mathematics
ISBN print 978-3-03719-159-0, ISBN online 978-3-03719-659-0
DOI 10.4171/159
March 2016, 363 pages, hardcover, 16.5 x 23.5 cm.
The book is intended as a companion to a one semester introductory lecture course on measure and integration. After an introduction to abstract measure theory it proceeds to the construction of the Lebesgue measure and of Borel measures on locally compact Hausdorff spaces, Lp
spaces and their dual spaces and elementary Hilbert space theory. Special features include the formulation of the Riesz Representation Theorem in terms of both inner and outer regularity, the proofs of the Marcinkiewicz Interpolation Theorem and the Calderon-Zygmund inequality as applications of Fubini’s theorem and Lebesgue differentiation, the treatment of the generalized Radon-Nikodym theorem due to Fremlin, and the existence proof for Haar measures. Three appendices deal with Urysohn’s Lemma, product topologies, and the inverse function theorem.
The book assumes familiarity with first year analysis and linear algebra. It is suitable for second year undergraduate students of mathematics or anyone desiring an introduction to the concepts of measure and integration.
sigma-Algebra, Lebesgue monotone convergence, Caratheodory criterion, Lebesgue
measure, Borel measure, Dieudonne’s measure, Riesz Representation Theorem,
Alexandrov Double Arrow Space, Sorgenfrey Line, separability, Cauchy-Schwarz
inequality, Jensen’s inequality, Egoroff’s theorem, Hardy’s inequality,
absolutely continuous measure, truly continuous measure, singular measure,
signed measure, Radon-Nikodym Theorem, Lebesgue Decomposition Theorem,
Hahn Decomposition Theorem, Jordan Decomposition Theorem, Hardy-Littlewood
maximal inequality, Vitali’s Covering Lemma, Lebesgue point, Lebesgue
Differentiation Theorem, Banach-Zarecki Theorem, Vitali?Caratheodory Theorem,
Cantor function, product sigma-algebra, Fubini’s Theorem, convolution,
Young’s inequality, mollifier, Marcinciewicz interpolation, Poisson identity,
Green’s formula, Calderon-Zygmund inequality, Haar measure, modular character.