An introduction to noncommutative spaces and their geometries

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Oliver Montenbruck, Thomas Pfleger

Astronomy on the PC provides practical solutions to a variety of astronomical problems. The book includes both astronomical fundamentals and the technical know-how for an implementation of high-quality software. Efficient and precise computer programs help the user to calculate and predict - positions of the Sun, Moon, and the planets - rising and setting times - physical ephemerides of the Sun and the major planets - positions of comets and minor planets (with perturbations) - the central line and local conditions of solar eclipses - stellar occultations - orbits in the solar system from three observations - coordinates from sky photographs Software developers will find a comprehensive collection of efficient Pascal routines. The extensive documentation and selfcontained structure facilitate a fast and reliable development of individual programs. The enclosed diskette contains source texts of all programs for Turbo Pascal on IBM-compatible PCs or Pure Pascal on Atari ST/TT computers. For the new edition the programs have also been made accessible using Windows. Furthermore, an input file for the OCCULT program is now included on the diskette containing the stars of the Zodiacal Catalogue by Robertson.

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Jean-Marie Souriau

This book is addressed to graduate students and researchers in mathematics and physics who are interested in mathematical and theoretical physics, symplectic geometry, mechanics, and (geometric) quantization. The aim of the book is to treat all three basic theories of physics, namely, classical mechanics, statistical mechanics, and quantum mechanics from the same perspective, that of symplectic geometry, thus showing the unifying power of the symplectic geometric approach. Reading this book will give the reader a deep understanding of the interrelationships between the three basic theories of physics. The first tow chapters provide the necessary mathematical background in differential geometry, Lie groups, and symplectic geometry. In Chapter 3 a coherent symplectic description of Galilean and relativistic mechanics is given, culminating in the classification of elementary particles (relativistic and non-relativistic, with or without spin, with or without mass). In Chapter 4 statistical mechanics is put into symplectic form, finishing with a symplectic description of the kinetic theory of gases and the computation of specific heats. Finally, in Chapter 5 the author presents his theory of geometric quantization. Highlights of this chapter are the derivations of various wave equations and the construction of the Fock space.

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Geoffrey M. Dixon

The four real division algebras (reals, complexes, quaternions and octonions) are the most obvious signposts to a rich and intricate realm of select and beautiful mathematical structures. Using the new tool of adjoint division algebras, with respect to which the division algebras themselves appear in the role of spinor spaces, some of these structures are developed, including parallelizable spheres, exceptional Lie groups, and triality. In the case of triality the use of adjoint octonions greatly simplifies its investigation. Motivating this work, however, is a strong conviction that the design of our physical reality arises from this select mathematical realm. A compelling case for that conviction is presented, a derivation of the standard model of leptons and quarks. The book will be of particular interest to particle and high energy theorists, and to applied mathematicians.

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N. Ida

Microwave testing has been paid only scant attention in the literature as a method for nondestructive testing of materials, yet it offers some attractive features, especially for the testing of composite and other non-metallic materials. Microwave techniques have been used in a large number of applications that can be classified as nondestructive testing applications, ranging from large scale remote sensing to detection of tumors in the body. This volume describes a unified approach to microwave nondestructive testing by presenting the three essential components of testing: theory, practice, and modelling. While recognizing that each of these subjects is wide enough to justify a volume of its own, the presentation of the three topics together shows that these are interrelated and should be practiced together. While few will argue against a good theoretical background, modelling and simulation of the testing environment is seldom part of the NDT training in any method, but particularly so in microwave testing. The text is devided in four parts. The first part presents the field theory background necessary for understanding the microwave domain. The second part treats microwave measurements as well as devices and sources and the third part discusses practical tests applicable to a variety of materials and geometries. The fourth part discusses modelling of microwave testing. Each chapter contains a bibliography intended to expand on the material given and, in particular, to point to subjects which could not be covered either as not appropriate or for lack of space. For engineers, applied physicsts, material scientists.