Series: The Frontiers Collection
2014, XIX, 250 p. 39 illus.
Hardcover
ISBN 978-3-642-45127-0
Due: January 15, 2014
First monograph devoted to the history of superstring theory
Objective presentation of a controversial area of physics enabling readers to see through the divisive hype and hysteria forming the 'String Wars'
Interweaves conceptual issues with the wider historical development
Reveals string theory's historically close connections with other areas of physics
Self-contained approach brings string theory within the grasp of non-specialists
During its forty year lifespan, string theory has always had the power to divide, being called both a 'theory of everything' and a 'theory of nothing'. Critics have even questioned whether it qualifies as a scientific theory at all. This book adopts an objective stance, standing back from the question of the truth or falsity of string theory and instead focusing on how it came to be and how it came to occupy its present position in physics. An unexpectedly rich history is revealed, with deep connections to our most well-established physical theories. Fully self-contained and written in a lively fashion, the book will appeal to a wide variety of readers from novice to specialist.
History and Mythology.- Part I: The (Very) Early Years: 1959-1973.- Particle Physics in the Sixties.- The Veneziano Model.- The Hadronic String.- Supersymmetric Strings and Field Theoretic Limits.- Part II: A Decade of Darkness: 1974-1984.- An Early Demise? Theoretical Exaptation in String Theory.- Turning Point(s).- Part III: String Theory Becomes Super: 1985-1995.- Superstring Theory and the Real World.- A 'Second Superstring Revolution' and the Future of String Theory.
Series: Applied Mathematical Sciences, Vol. 82
3rd ed. 2014, XVI, 412 p. 1 illus.
Hardcover
ISBN 978-1-4614-9592-5
.Complete basis in functional analysis including the Hahn-Banach and the open mapping theorem
More on boundary integral equations in Sobolev spaces
New developements in collocation methods via trigononmetric polynomials
This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter.
For this third edition in order to make the introduction to the basic functional analytic tools more complete the Hahn?Banach extension theorem and the Banach open mapping theorem are now included in the text.The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods
Normed Spaces.- Bounded and Compact Operators.- Riesz Theory.- Dual Systems and Fredholm Alternative.- Regularization in Dual Systems.- Potential Theory.- Singular Integral Equations.- Sobolev Spaces.- The Heat Equation.- Operator Approximations .-Degenerate Kernel Approximation.- Quadrature Methods.- Projection Methods.- Iterative Solution and Stability.- Equations of the First Kind.- Tikhonov Regularization.- Regularization by Discretization.- Inverse Boundary Value Problems.- References.- Index.
Series: Lecture Notes in Mathematics, Vol. 2104
2014, X, 180 p. 13 illus., 6 illus. in color.
Softcover
ISBN 978-3-319-04074-5
Due: February 28, 2014
Contains a comprehensive introduction to the theory of Teichmuller curves
Is kept as self-contained as possible
Contains 15 figures and 2 tables
These notes introduce a new class of algebraic curves on Hilbert modular surfaces. These curves are called twisted Teichmuller curves, because their construction is very reminiscent of Hirzebruch-Zagier cycles. These new objects are analyzed in detail and their main properties are described. In particular, the volume of twisted Teichmuller curves is calculated and their components are partially classified. The study of algebraic curves on Hilbert modular surfaces has been widely covered in the literature due to their arithmetic importance. Among these, twisted diagonals (Hirzebruch-Zagier cycles) are some of the most important examples.
Introduction.- Background.- Teichmuller Curves.- Twisted Teichmuller Curves.- Stabilizer and Maximality.- Calculations for Twisted Teichmuller Curves.- Prym Varieties and Teichmuller Curves.- Lyapunov Exponents.- Kobayashi Curves Revisited.- Appendix.- Tables.- List of Symbols.- Index.- Bibliography.
Series: Lecture Notes in Mathematics, Vol. 2106
Subseries: Ecole d'Ete de Probabilites de Saint-Flour
2014, Approx. 170 p. 20 illus., 4 illus. in color.
Softcover
ISBN 978-3-319-04393-7
Due: March 31, 2014
Contains interesting examples of couplings
Gentle introduction to Brownian motion and analysis
Heuristic explanations of the main results
These lecture notes provide an introduction to the applications of Brownian motion to analysis and, more generally, connections between Brownian motion and analysis. Brownian motion is a well-suited model for a wide range of real random phenomena, from chaotic oscillations of microscopic objects, such as flower pollen in water, to stock market fluctuations. It is also a purely abstract mathematical tool which can be used to prove theorems in "deterministic" fields of mathematics.
The notes include a brief review of Brownian motion and a section on probabilistic proofs of classical theorems in analysis. The bulk of the notes are devoted to recent (post-1990) applications of stochastic analysis to Neumann eigenfunctions, Neumann heat kernel and the heat equation in time-dependent domains.
1. Brownian motion.- 2. Probabilistic proofs of classical theorems.- 3. Overview of the "hot spots" problem.- 4. Neumann eigenfunctions and eigenvalues.- 5. Synchronous and mirror couplings.- 6. Parabolic boundary Harnack principle.- 7. Scaling coupling.- 8. Nodal lines.- 9. Neumann heat kernel monotonicity.- 10. Reflected Brownian motion in time dependent domains.
Series: Lecture Notes in Mathematics, Vol. 2105
2014, Approx. 220 p.
Softcover
ISBN 978-3-319-04416-3
Due: April 21, 2014
Provides rapid access to advanced Rigid Geometry
Offers self-contained content
Includes Tate’s classical theory, as well as Raynaud’s approach using formal schemes
A first version of this work appeared in 2005 as a Preprint of the Collaborative Research Center "Geometrical Structures in Mathematics" at the University of Munster. Its aim was to offer a concise and self-contained 'lecture-style' introduction to the theory of classical rigid geometry established by John Tate, together with the formal algebraic geometry approach launched by Michel Raynaud. These Lectures are now viewed commonly as an ideal means of learning advanced rigid geometry, regardless of the reader's level of background. Despite its parsimonious style, the presentation illustrates a number of key facts even more extensively than any other previous work.
This Lecture Notes Volume is a revised and slightly expanded version of the original preprint and has been published at the suggestion of several experts in the field.
Classical Rigid Geometry.- Tate Algebras.- Affinoid Algebras and their Associated Spaces.- Affinoid Functions.- Towards the Notion of Rigid Spaces.- Coherent Sheaves on Rigid Spaces.- Formal Geometry.- Adic Rings and their Associated Formal Schemes.- Raynaud's View on Rigid Spaces.- More Advanced Stuff.- Appendix.- References.- Index.
Series: Universitext
2014, X, 339 p. 3 illus.
Softcover
ISBN 978-3-319-04149-0
Due: February 28, 2014
Based on the lectures from the Graduate School of Information Sciences of Tohoku University and the Budapest University of Technology and Economics
Provides a strong emphasis to various areas of quantum theory, particularly quantum information theory
Covers classical topics and recent advances in the field
Matrices can be studied in different ways. They are a linear algebraic structure and have a topological/analytical aspect (for example, the normed space of matrices) and they also carry an order structure that is induced by positive semidefinite matrices. The interplay of these closely related structures is an essential feature of matrix analysis.
This book explains these aspects of matrix analysis from a functional analysis point of view. After an introduction to matrices and functional analysis, it covers more advanced topics such as matrix monotone functions, matrix means, majorization and entropies. Several applications to quantum information are also included.
Introduction to Matrix Analysis and Applications is appropriate for an advanced graduate course on matrix analysis, particularly aimed at studying quantum information. It can also be used as a reference for researchers in quantum information, statistics, engineering and economics.
Fundamentals of operators and matrices.- Mappings and algebras.- Functional calculus and derivation.- Matrix monotone functions and convexity.- Matrix means and inequalities.- Majorization and singular values.- Some applications.