Mathematical & Computational

This book deals with 2-spinors in general relativity, beginning by developing spinors in a geometrical way rather than using representation theory, which can be a little abstract. This gives the reader greater physical intuition into the way in which...

Mathematics is the language of physics, and over time physicists have developed their own dialect. The main purpose of this book is to bridge this language barrier, and introduce the readers to the beauty of mathematical physics. It shows how to combine...

A ground-breaking and practical treatment of probability and stochastic processes A Modern Theory of Random Variation is a new and radical re-formulation of the mathematical underpinnings of subjects as diverse as investment, communication engineering,...

This volume consists of four contributions that are based on a series of lectures delivered by Jens Frehse. Konstantin Pikeckas, K.R. Rajagopal and Wolf von Wahl t the Fourth Winter School in Mathematical Theory in Fluid Mechanics, held in Paseky, Czech...

Using real-life applications, this graduate-level textbook introduces different mathematical methods of scientific computation to solve minimization problems using examples ranging from locating an aircraft, finding the best time to replace a computer,...

Supersymmetry (SUSY) is one of the most important ideas ever conceived in particle physics. It is a symmetry that relates known elementary particles of a certain spin to as yet undiscovered particles that differ by half a unit of that spin (known as...

This book contains MATLAB programs to demonstrate the numerical algorithms, the analytical approaches, and the physical principles. It starts with single particle, single fluid, and single wave, then the kinetic theory, the transport, the...

This book constitutes the proceedings of the 2000 Howard conference on "Infinite Dimensional Lie Groups in Geometry and Representation Theory". It presents some important recent developments in this area. It opens with a topological...

This book introduces a variety of aspects in nonperturbative Quantum Chromodynamics (QCD), focusing on the topological objects present in gauge theories. These objects, like magnetic monopoles, instantons, instanto-dysons, sphalerons, QCD flux tubes,...

This book provides a broad introduction to gauge field theories formulated on a space-time lattice, and in particular of QCD. It serves as a textbook for advanced graduate students, and also provides the reader with the necessary analytical and numerical...

This book offers an informal, easy-to-understand account of topics in modern physics and mathematics. The focus is, in particular, on statistical mechanics, soft matter, probability, chaos, complexity, and models, as well as their interplay. The book...

From classical mechanics and classical electrodynamics to modern quantum mechanics many physical phenomena are formulated in terms of similar partial differential equations while boundary conditions determine the specifics of the problem. This 45th...

This book is a compilation of different methods of formulating and solving inverse problems in physics from classical mechanics to the potentials and nucleus-nucleus scattering. Mathematical proofs are omitted since excellent monographs already exist...

This 2002 book discusses the classical foundations of field theory, using the language of variational methods and covariance. It explores the limits of what can be achieved with purely classical notions, and shows how these have a deep and important...

Surely the reader had come across situations where he would have given his life to get the "final answer", the reason for our existence, a Theory of Everything, a true World Formula that contains it all... So did the author of this book. There was this...

Providing a detailed and pedagogical account of the rapidly-growing field of computational statistical physics, this book covers both the theoretical foundations of equilibrium and non-equilibrium statistical physics, and also modern, computational...

This new edition of Conceptual Developments of 20th Century Field Theories explores the conceptual foundations and historical roots of fundamental field theories. It also uncovers the underlying issues, logic and dynamics in fundamental physics. In...

This highly pedagogical textbook for graduate students in particle, theoretical and mathematical physics, explores advanced topics of quantum field theory. Clearly divided into two parts; the first focuses on instantons with a detailed exposition of...

This graduate-level text gives a self-contained exposition of fundamental topics in equilibrium and nonequilibrium statistical thermodynamics. The text follows a balanced approach between the macroscopic (thermodynamic) and microscopic (statistical)...

Path integrals provide a powerful method for describing quantum phenomena. This book introduces the quantum mechanics of particles that move in curved space by employing path integrals and then using them to compute anomalies in quantum field theories...

This volume compiles notes from four mini courses given at the summer school on asymptotic analysis in general relativity, held at the Institut Fourier in Grenoble, France. It contains an up-to-date panorama of modern techniques in the asymptotic...

Simulation technology, and computational fluid dynamics (CFD) in particular, is essential in the search for solutions to the modern challenges faced by humanity. Revolutions in CFD over the last decade include the use of unstructured meshes, permitting...

In the period between the birth of quantum mechanics and the late 1950s, V.A. Fock wrote papers that are now deemed classics. In his works on theoretical physics, Fock not only skillfully applied advanced analytical and algebraic methods, but also...

This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. One...

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,...

The theory of soliton equations and integrable systems has developed rapidly during the last 30 years with numerous applications in mechanics and physics. For a long time, books in this field have not been written but the flood of papers was...

The book covers different aspects of mathematical methods for Physics. It is designed for graduate courses but a part of it can also be used by undergraduate students. The leitmotiv of the book is the search for a common mathematical framework for a wide...

Statistical mechanics forms the basis of the study of the properties of matter in bulk from a molecular or microscopic viewpoint. This 1966 edition of the late Sir Ralph Fowler's monumental exposition of the subject was one of the first to adopt a...

This book reviews one-dimensional reactions, dynamics, diffusion and adsorption. In studies of complex systems in biology, chemistry and physics, understanding can be gained by analytical and numerical analyses of simple models. This book presents review...

Research and development in the pioneering field of quantum computing involve just about every facet of science and engineering, including the significant areas of mathematics and physics. Based on the firm understanding that mathematics and physics are...

This book teaches you all necessary (problem-independent) tools and techniques needed to implement and perform sophisticated scientific numerical simulations. Thus, it is suited for undergraduate and graduate students who want to become experts in...

This volume contains survey articles on various aspects of stochastic partial differential equations (SPDEs) and their applications in stochastic control theory and in physics.The topics presented in this volume are:This book is intended not only for...

This textbook explains the fundamental concepts and techniques of group theory by making use of language familiar to physicists. Calculation methods in the context of physics are emphasized. New materials drawn from the teaching and research experience...

In this volume, topics are drawn from field theory, especially gauge field theory, as applied to particle, condensed matter and gravitational physics, and concern a variety of interesting subjects. These include geometricalDtopological effects in quantum...

Mathematical physics has made enormous strides over the past few decades, with the emergence of many new disciplines and with revolutionary advances in old disciplines. One of the especially interesting features is the link between developments in...

Starting with the basics of Hamiltonian dynamics and canonical transformations, this text follows the historical development of the theory culminating in recent results: the Kolmogorov-Arnold-Moser theorem, Nekhoroshev's theorem and superexponential...

Lie's group theory of differential equations unifies the many ad hoc methods known for solving differential equations and provides powerful new ways to find solutions. The theory has applications to both ordinary and partial differential equations and is...

This unique book complements traditional textbooks by providing a visual yet rigorous survey of the mathematics used in theoretical physics beyond that typically covered in undergraduate math and physics courses. The exposition is pedagogical but...

This graduate-level text gives a self-contained exposition of fundamental topics in equilibrium and nonequilibrium statistical thermodynamics. The text follows a balanced approach between the macroscopic (thermodynamic) and microscopic (statistical)...

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