Division algebras

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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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Giovanni Landi

These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'*-algebras, module theory and K-theory, spectral calculus, forms and connection theory. Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated. Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content. This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics.

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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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Eric Yoder and Natalie Yoder

65 short mysteries introduce readers to science facts ranging from the life, earth and space, physical and chemical, to the general sciences. Tap into your science wisdom and critical thinking skills to solve these brainteasers!