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The subject of this book is the Casimir effect, a manifestation of zero-point oscillations of the quantum vacuum resulting in forces acting between closely spaced bodies. For the benefit of the reader, the book assembles field-theoretical foundations of this phenomenon, applications of the general theory to real materials, and a comprehensive description of all recently performed measurements of the Casimir force with a comparison between experiment and theory. There is an urgent need for a book of this type, given the increase of interest in forces originating from the quantum vacuum. Numerous new results have been obtained in the last few years which are not reflected in previous books on the subject, but which are very promising for fundamental science and nanotechnology. The book is a unique source of information presenting a critical assessment of all the main results and approaches from hundreds of journal papers. It also outlines new ideas which have not yet been universally accepted but which are finding increasing support from experiment.
Unique in its clarity, examples and range, Physical Mathematics explains as simply as possible the mathematics that graduate students and professional physicists need in their courses and research. The author illustrates the mathematics with numerous physical examples drawn from contemporary research. In addition to basic subjects such as linear algebra, Fourier analysis, complex variables, differential equations and Bessel functions, this textbook covers topics such as the singular-value decomposition, Lie algebras, the tensors and forms of general relativity, the central limit theorem and Kolmogorov test of statistics, the Monte Carlo methods of experimental and theoretical physics, the renormalization group of condensed-matter physics and the functional derivatives and Feynman path integrals of quantum field theory.
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A modern and comprehensive textbook intended to correct the lack of such a text in times of the ever-increasing importance of the subject in contemporary science, technology, and everyday life. With its clear pedagogical presentation and with many examples and solved problems it is useful for physics students, researchers and teachers alike.
Includes entries for maps and atlases.
This book is the result of several years of work by the authors on different aspects of zeta functions and related topics. The aim is twofold. On one hand, a considerable number of useful formulas, essential for dealing with the different aspects of zeta-function regularization (analytic continuation, asymptotic expansions), many of which appear here, in book format, for the first time are presented. On the other hand, the authors show explicitly how to make use of such formulas and techniques in practical applications to physical problems of very different nature. Virtually all types of zeta functions are dealt with in the book.
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