The spinor calculus employed in general relativity is a very useful tool; many expressions and computations are considerably simplified if one makes use of spinors instead of tensors. Some advantages of the spinor formalism applied in the four-dimensional space-time of general relativity come from the fact that each spinor index takes two values only, which simplifies the algebraic manipulations. Spinors for spaces of any dimension can be defined in connection with rep resentations of orthogonal groups and in the case of spaces of dimension three, the spinor indices also take two values only,...

Astronomers do not do experiments. They observe the universe primarily through detect ing light emitted by stars and other luminous objects. Since this light must travel through space to reach us, variations in the metric of space affects the appearance of astronomical objects. These variations lead to dramatic changes in the shape and brightness of astronom ical sources. Because these variations are sensitive to mass rather than to light, observations of gravitational lensing enable astronomers to probe the mass distribution of the universe. With gravitational lensing observations,...

Disorder is one of the central topics in science today. Over the past 15 years various aspects of the effects of disorder have changed a number of paradigms in mathematics and physics. One such effect is a phenomenon called localization, which describes the very strange behaviour of waves in random media. Instead of travelling through space as they do in ordered environments, localized waves stay in a confined region and are caught by disorder. This work is the first treatment of the subject in monograph or textbook form.

In this book we display the fundamental structure underlying classical electro dynamics, i. e., the phenomenological theory of electric and magnetic effects. The book can be used as a textbook for an advanced course in theoretical electrodynamics for physics and mathematics students and, perhaps, for some highly motivated electrical engineering students. We expect from our readers that they know elementary electrodynamics in the conventional (1 + 3)-dimensional form including Maxwell's equations. More over, they should be familiar with linear algebra and elementary analysis, in cluding vector...

'MathPhys Odyssey 2001' will serve as an excellent reference text for mathematical physicists and graduate students in a number of areas.; Kashiwara/Miwa have a good track record with both SV and Birkhauser.

Across the centuries, the development and growth of mathematical concepts have been strongly stimulated by the needs of mechanics. Vector algebra was developed to describe the equilibrium of force systems and originated from Stevin's experiments (1548-1620). Vector analysis was then introduced to study velocity fields and force fields. Classical dynamics required the differential calculus developed by Newton (1687). Nevertheless, the concept of particle acceleration was the starting point for introducing a structured spacetime. Instantaneous velocity involved the set of particle positions in...

Dirac operators play an important part in several domains of mathematics and mathematical physics, for example: index theory, theory of elliptic pseudodifferential operators, theory of electromagnetism, particle physics, and representation theory of Lie groups. In this work, the basic theories underlying the concept of Dirac operators are explored. Starting with the requisite material on Clifford algebras and differential geometry, the text focuses on the two main properties of Dirac operators: conformal invariance, which determines the local behavior of the operator, and the unique...

This self-contained text presents quantum mechanics from the point of view of some computational examples with a mixture of mathematical clarity often not found in texts offering only a purely physical point of view. Emphasis is placed on the systematic application of the Nikiforov-- Uvarov theory of generalized hypergeometric differential equations to solve the Schr"dinger equation and to obtain the quantization of energies from a single unified point of view.

Themainobjectiveofthisbookistogiveacollectionofcriteriaavailablein the spectral theory of selfadjoint operators, and to identify the spectrum and its components in the Lebesgue decomposition. Many of these criteria were published in several articles in di?erent journals. We collected them, added some and gave some overview that can serve as a platform for further research activities. Spectral theory of Schr] odinger type operators has a long history; however the most widely used methods were limited in number. For any selfadjoint operatorA on a separable Hilbert space the spectrum is...