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Quantum Geometry, Matrix Theory, and Gravity
Building on mathematical structures familiar from quantum mechanics, this book provides an introduction to quantization in a broad context before developing a framework for quantum geometry in Matrix Theory and string theory. Taking a physics-oriented approach to quantum geometry, this framework helps explain the physics of Yang–Mills-type matrix models, leading to a quantum theory of space-time and matter. This novel framework is then applied to Matrix Theory, which is defined through distinguished maximally supersymmetric matrix models related to string theory. A mechanism for gravity is discussed in depth, which emerges as a quantum effect on quantum space-time within Matrix Theory. Using explicit examples and exercises, readers will develop a physical intuition for the mathematical concepts and mechanisms. It will benefit advanced students and researchers in theoretical and mathematical physics, and is a useful resource for physicists and mathematicians interested in the geometrical aspects of quantization in a broader context.
Special Matrices Of Mathematical Physics: Stochastic, Circulant And Bell Matrices
This book expounds three special kinds of matrices that are of physical interest, centering on physical examples. Stochastic matrices describe dynamical systems of many different types, involving (or not) phenomena like transience, dissipation, ergodicity, nonequilibrium, and hypersensitivity to initial conditions. The main characteristic is growth by agglomeration, as in glass formation. Circulants are the building blocks of elementary Fourier analysis and provide a natural gateway to quantum mechanics and noncommutative geometry. Bell polynomials offer closed expressions for many formulas concerning Lie algebra invariants, differential geometry and real gases, and their matrices are instrumental in the study of chaotic mappings.
Formulations of General Relativity
Carefully documenting the different formulations of general relativity, the author reveals valuable insight into the nature of the gravitational force and its interaction with matter. This book will interest graduate students and researchers in the fields of general relativity, gravitational physics and differential geometry.
Transactions of the International Astronomical Union
IAU Transactions XXIIB summarizes the work of the XXIInd General Assembly. The discourses given during the Inaugural and Closing Ceremonies are reproduced in Chapters I and III, respectively. The proceedings of the two sessions of the General Assembly will be found in Chapter II, which includes the Resolutions and the report of the Finance Committee. The Statutes, Bye-Laws and a few working rules of the Union are published in Chapter IV. The Accounts and other aspects of the administration of the Union are recorded in Chapter V, together with the report of the Executive Committee for this last triennium, and provide the permanent record for the Union in the period 1991-1994. This volume also contains the Commission reports from The Hague compiled by the Presidents of the Commissions (Chapter VI). Finally, Chapter VII contains the list of countries adhering to the Union and the alphabetical, geographical and commission membership lists of about 8000 individual members. The IAU still appears to be unique among the scientific Unions in maintaining this category of individual membership which contributes in a crucial way to the spirit and the aims of the Union.
Transactions of the International Astronomical Union
The XXth General Assembly of the International Astronomical Union was held in Baltimore, Maryland USA from August 02 to 11, 1988. The Inaugural Ceremony on August 02 was held in the presence of representatives of the United States Governn:ent, t~e S~ate of Maryland, the City of Baltimore and the host institution -the Johns Hopkins Umverslty- as well as of the National and Local Organising Committees. The scientific programme maintained the high standards of the Union and the scientific proceedings may be found either in this volume or in volume 8 of Highlights of Astronomy. The scientific programme was organised by the 40 Commission Presidents and coordinated by the General Secretary (1985-1988), Dr. J.-P. Swings. The local arrangements were effectively made through the National Organising Committee under the Chairmanship of Prof. F. Drake and the Local Organising Committee under the co-Chairmanship of Prof. A. Oavidsen and Dr. R. Giacconi. The smooth day to day operation of the meeting resulted from the incomparable dedication of Karen Weinstock and Harold Screen.
Tenth Marcel Grossmann Meeting, The: On Recent Developments In Theoretical & Experimental General Relativity, Gravitation, & Relativistic Field Theories (In 3 Vols) - Procs Of The Mgio Meeting Held At Brazilian Ctr For Res In Phys (Cbpf)
The Marcel Grossmann meetings were conceived to promote theoretical understanding in the fields of physics, mathematics, astronomy and astrophysics and to direct future technological, observational, and experimental efforts. They review recent developments in gravitation and general relativity, with major emphasis on mathematical foundations and physical predictions. Their main objective is to bring together scientists from diverse backgrounds and their range of topics is broad, from more abstract classical theory and quantum gravity and strings to more concrete relativistic astrophysics observations and modeling.This Tenth Marcel Grossmann Meeting was organized by an international committee...
GROUP 24
One of the most enduring elements in theoretical physics has been group theory. GROUP 24: Physical and Mathematical Aspects of Symmetries provides an important selection of informative articles describing recent advances in the field. The applications of group theory presented in this book deal not only with the traditional fields of physics, but also include such disciplines as chemistry and biology. Awarded the Wigner Medal and the Weyl Prize, respectively, H.J. Lipkin and E. Frenkel begin the volume with their contributions. Plenary session contributions are represented by 18 longer articles, followed by nearly 200 shorter articles. The book also presents coherent states, wavelets, and applications and quantum group theory and integrable systems in two separate sections. As a record of an international meeting devoted to the physical and mathematical aspects of group theory, GROUP 24: Physical and Mathematical Aspects of Symmetries constitutes an essential reference for all researchers interested in various current developments related to the important concept of symmetry.
The Tenth Marcel Grossmann Meeting
The Marcel Grossmann meetings were conceived to promote theoretical understanding in the fields of physics, mathematics, astronomy and astrophysics and to direct future technological, observational, and experimental efforts. They review recent developments in gravitation and general relativity, with major emphasis on mathematical foundations and physical predictions. Their main objective is to bring together scientists from diverse backgrounds and their range of topics is broad, from more abstract classical theory and quantum gravity and strings to more concrete relativistic astrophysics observations and modeling. This Tenth Marcel Grossmann Meeting was organized by an international committe...
An Introduction to Geometrical Physics
This book focuses on the unifying power of the geometrical language in bringing together concepts from many different areas of physics, ranging from classical physics to the theories describing the four fundamental interactions of Nature -- gravitational, electromagnetic, strong nuclear, and weak nuclear. The book provides in a single volume a thorough introduction to topology and differential geometry, as well as many applications to both mathematical and physical problems. It is aimed as an elementary text and is intended for first year graduate students. In addition to the traditional contents of books on special and general relativities, this book discusses also some recent advances such as de Sitter invariant special relativity, teleparallel gravity and their implications in cosmology for those wishing to reach a higher level of understanding.
