It would seem that any specialist in plasma physics studying a medium in which the interaction between particles is as distance-dependent as the inter action between stars and other gravitating masses would assert that the role of collective effects in the dynamics of gravitating systems must be decisive. However, among astronomers this point of view has been recog nized only very recently. So, comparatively recently, serious consideration has been devoted to theories of galactic spiral structure in which the dominant role is played by the orbital properties of individual stars rather than collec tive effects. In this connection we would like to draw the reader's attention to a difference in the scientific traditions of plasma physicists and astrono mers, whereby the former have explained the delay of the onset of controlled thermonuclear fusion by the "intrigues" of collective processes in the plasma, while many a generation of astronomers were calculating star motions, solar and lunar eclipses, and a number of other fine effects for many years ahead by making excellent use of only the laws of Newtonian mechanics. Therefore, for an astronomer, it is perhaps not easy to agree with the fact that the evolution of stellar systems is controlled mainly by collective effects, and the habitual methods of theoretical mechanics III astronomy must make way for the method of self-consistent fields.

This book is written to bring out the physical content behind the mathematical formulae.

This book deals with an important class of many-body systems: those where the interaction potential decays slowly for large inter-particle distances; in particular, systems where the decay is slower than the inverse inter-particle distance raised to the dimension of the embedding space. Gravitational and Coulomb interactions are the most prominent examples, however it has become clear that long-range interactions are more common than previously thought. A satisfactory understanding of properties, generally considered as oddities only a couple of decades ago, has now been reached: ensemble inequivalence, negative specific heat, negative susceptibility, ergodicity breaking, out-of-equilibrium quasi-stationary-states, anomalous diffusion. The book, intended for Master and PhD students, tries to gradually acquaint the reader with the subject. The first two parts describe the theoretical and computational instruments needed to address the study of both equilibrium and dynamical properties of systems subject to long-range forces. The third part of the book is devoted to applications of such techniques to the most relevant examples of long-range systems.

A unique graduate textbook that develops powerful approximation methods and their applications to real-life astrophysical systems.

This book formulates a unified approach to the description of many-particle systems combining the methods of statistical physics and quantum field theory. The benefits of such an approach are in the description of phase transitions during the formation of new spatially inhomogeneous phases, as well in describing quasi-equilibrium systems with spatially inhomogeneous particle distributions (for example, self-gravitating systems) and metastable states.The validity of the methods used in the statistical description of many-particle systems and models (theory of phase transitions included) is discussed and compared. The idea of using the quantum field theory approach and related topics (path integration, saddle-point and stationary-phase methods, Hubbard-Stratonovich transformation, mean-field theory, and functional integrals) is described in detail to facilitate further understanding and explore more applications.To some extent, the book could be treated as a brief encyclopedia of methods applicable to the statistical description of spatially inhomogeneous equilibrium and metastable particle distributions. Additionally, the general approach is not only formulated, but also applied to solve various practically important problems (gravitating gas, Coulomb-like systems, dusty plasmas, thermodynamics of cellular structures, non-uniform dynamics of gravitating systems, etc.).

This book addresses a fascinating set of questions in theoretical physics which will both entertain and enlighten all students, teachers and researchers and other physics aficionados. These range from Newtonian mechanics to quantum field theory and cover several puzzling issues that do not appear in standard textbooks. Some topics cover conceptual conundrums, the solutions to which lead to surprising insights; some correct popular misconceptions in the textbook discussion of certain topics; others illustrate deep connections between apparently unconnected domains of theoretical physics; and a few provide remarkably simple derivations of results which are not often appreciated. The connoisseur of theoretical physics will enjoy a feast of pleasant surprises skilfully prepared by an internationally acclaimed theoretical physicist. Each topic is introduced with proper background discussion and special effort is taken to make the discussion self-contained, clear and comprehensible to anyone with an undergraduate education in physics.