As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures on a variety of problems in nonlinear functional analysis and its applications. In doing this, I have recommended to my students a number of excellent monographs devoted to specialized topics, but there was no complete survey-type exposition of nonlinear functional analysis making available a quick survey to the wide range of readers including mathematicians, natural scientists, and engineers who have only an elementary knowledge of linear...
As long as a branch of knowledge offers an abundance of problems, it is full of vitality. David Hilbert Over the last 15 years I have given lectures o...
A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability. Albert Einstein There are two different ways of teaching mathematics, namely, (i) the systematic way, and (ii) the application-oriented way. More precisely, by (i), I mean a systematic presentation of the material governed by the desire for mathematical perfection and completeness of the results. In contrast to (i), approach (ii) starts out from the question "What are the most important applications?" and then tries to answer this question...
A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicabi...
A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicability. Albert Einstein There are two different ways of teaching mathematics, namely, (i) the systematic way, and (ii) the application-oriented way. More precisely, by (i), I mean a systematic presentation of the material governed by the desire for mathematical perfection and completeness of the results. In contrast to (i), approach (ii) starts out from the question "What are the most important applications?" and then tries to answer this question...
A theory is the more impressive, the simpler are its premises, the more distinct are the things it connects, and the broader is its range of applicabi...
This Edited Volume is based on a workshop on Mathematical and Physical - pects of Quantum Gravity held at the Heinrich-Fabri Institute in Blaubeuren st (Germany) from July 28th to August 1, 2005. This workshop was the succ- sor of a similar workshop held at the same place in September 2003 on the issue of Mathematical and Physical Aspects of Quantum Field Theories . Both wo- shops were intended to bring together mathematicians and physicists to discuss profoundquestionswithin the non-emptyintersectionofmathematics andphysics. The basic idea of this series of workshops is to cover a broad...
This Edited Volume is based on a workshop on Mathematical and Physical - pects of Quantum Gravity held at the Heinrich-Fabri Institute in Blaubeuren s...
The greatest mathematicians, such as Archimedes, Newton, and Gauss, always united theory and applications in equal measure. Felix Klein There exists the remarkable possibility that one can master a subject mathemati- cally, without really understanding its essence. Albert Einstein Don't give us numbers: give us insight A contemporary natural scientist to a mathematician Numerous questions in physics, chemistry, biology, and economics lead to nonlinear problems; for example, deformation of rods, plates, and shells; behavior of plastic materials; surface waves of fluids; flows around objects...
The greatest mathematicians, such as Archimedes, Newton, and Gauss, always united theory and applications in equal measure. Felix Klein There exists t...
And God said, Let there be light; and there was light. Genesis 1,3 Light is not only the basis of our biological existence, but also an essential source of our knowledge about the physical laws of nature, ranging from the seventeenth century geometrical optics up to the twentieth century theory of general relativity and quantum electrodynamics. Folklore Don t give us numbers: give us insight A contemporary natural scientist to a mathematician The present book is the second volume of a comprehensive introduction to themathematicalandphysicalaspectsofmodernquantum?eldtheorywhich comprehends...
And God said, Let there be light; and there was light. Genesis 1,3 Light is not only the basis of our biological existence, but also an essential sour...
1 Dass ich erkenne, was die Welt im Innersten zusammenh] alt. Faust Concepts without intuition are empty, intuition without concepts is blind. Immanuel Kant (1724 1804) The greatest mathematicians like Archimedes, Newton, and Gauss have always been able to combine theory and applications into one. Felix Klein (1849 1925) The present comprehensive introduction to the mathematical and physical aspects of quantum ?eld theory consists of the following six volumes: Volume I: Basics in Mathematics and Physics Volume II: Quantum Electrodynamics Volume III: Gauge Theory Volume IV: Quantum Mathematics...
1 Dass ich erkenne, was die Welt im Innersten zusammenh] alt. Faust Concepts without intuition are empty, intuition without concepts is blind. Immanue...
The main concern in all scientific work must be the human being himsel This, one should never forget among all those diagrams and equations. Albert Einstein This volume is part of a comprehensive presentation of nonlinear functional analysis, the basic content of which has been outlined in the Preface of Part I. A Table of Contents for all five volumes may also be found in Part I. The Part IV and the following Part V contain applications to mathematical present physics. Our goals are the following: (i) A detailed motivation of the basic equations in important disciplines of theoretical...
The main concern in all scientific work must be the human being himsel This, one should never forget among all those diagrams and equations. Albert E...
One of the most challenging problems of contemporary theoretical physics is the mathematically rigorous construction of a theory which describes gravitation and the other fundamental physical interactions within a common framework. The physical ideas which grew from attempts to develop such a theory require highly advanced mathematical methods and radically new physical concepts.
This book presents different approaches to a rigorous unified description of quantum fields and gravity. It contains a carefully selected cross-section of lively discussions which took place in autumn 2010 at...
One of the most challenging problems of contemporary theoretical physics is the mathematically rigorous construction of a theory which describes gr...
This is the third volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced undergraduate students to professional scientists. This books seeks to bridge the existing gap between the different languages used by mathematicians and physicists. §For students of mathematics it is shown that detailed knowledge of the physical background helps to discover interesting interrelationships between quite diverse mathematical topics. For students of physics fairly advanced mathematics, beyond that included in the usual curriculum in...
This is the third volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists ranging from advanced und...
