This work provides a unique introduction to the theory of complex angular momenta, based on the methods of field theory. It comprises an English translation of a lecture course given by Vladimir Gribov in 1969. Besides their historical significance, these lectures contain material highly relevant to research today and likely to form the basis for future developments in the subject.

The scalar-tensor theory of gravitation moved into the limelight in recent years due to developments in string theory, M-theory and "brane world" constructions. This book introduces the subject at a level suitable for both graduate students and researchers. It explores scalar fields, placing them in context with a discussion of Brans-Dicke theory, covering the cosmological constant problem, higher dimensional space-time, branes and conformal transformations.

Calculations of relativistic hydrodynamics are crucial to several areas of current research in the physics of supernovae and stellar collapse. This book provides an overview of the computational framework in which such calculations have been developed, with examples of applications to real physical systems. Beginning with the development of the equations and differencing schemes for special relativistic hydrodynamics, the book stresses the viability of the Euler-Lagrange approach to most astrophysical problems. It details aspects of solving the Einstein equations together with the fluid...

Comprehensive survey of static topological solitons and their dynamical interactions, for graduates and researchers.

This text describes the gravitational interactions and evolution of astronomical systems on all scales, from small groups of stars through galaxies and clusters of galaxies to the Universe itself. In a rapidly developing area of astronomy, it is the first comprehensive treatise on the subject to be published since the early 1960s. Concentrating on the basic physics, at a graduate student level, it also develops many astronomical applications in considerable detail. The book is self-contained. Most results are derived from preceding ones in a straightforward way. It is written to bring out the...

Kinetic Theory in the Expanding Universe is a self-contained exposition of the applications of kinetic theory to basic problems in modern cosmology, such as the role of stable and unstable massive neutrinos and the theory of cosmological helium production. There has been rapid development of the theory of the origin and evolution of the universe in recent years, stimulated, in large part, by new observations and theories in astrophysics and particle physics. Bernstein takes a different approach and studies what can be concluded from the application of kinetic theory, and in particular the...

This is a concise graduate level introduction to analytical functional methods in quantum field theory. Functional integral methods provide relatively simple solutions to a wide range of problems in quantum field theory. After introducing the basic mathematical background, this book goes on to study applications and consequences of the formalism to the study of series expansions, measure, phase transitions, physics on spaces with nontrivial topologies, stochastic quantisation, fermions, QED, non-abelian gauge theories, symmetry breaking, the effective potential, finite temperature field...

Using a self-contained and concise treatment of modern differential geometry, this book will be of great interest to graduate students and researchers in applied mathematics or theoretical physics working in field theory, particle physics, or general relativity. The authors begin with an elementary presentation of differential forms. This formalism is then used to discuss physical examples, followed by a generalization of the mathematics and physics presented to manifolds. The book emphasizes the applications of differential geometry concerned with gauge theories in particle physics and...

This text introduces the theory of Hamiltonian chaos, outlines the main results in the field, and goes on to consider implications for quantum mechanics.

The study of nonlinear dynamics, and in particular of chaotic systems, is one of the fastest growing and productive areas in physics and applied mathematics. In its first six chapters, this timely book introduces the theory of classical Hamiltonian systems. The aim is not to be comprehensive, but rather to provide a starting point for further investigation. The main focus is on periodic orbits and their neighborhood, since this approach is...

This is an updated and expanded second edition of a successful and well-reviewed text presenting a detailed exposition of the modern theory of supermanifolds, including a rigorous account of the super-analogs of all the basic structures of ordinary manifold theory. The exposition opens with the theory of analysis over supernumbers (Grassman variables), Berezin integration, supervector spaces and the superdeterminant. This basic material is then applied to the theory of supermanifolds, with an account of super-analogs of Lie derivatives, connections, metric, curvature, geodesics, Killing...