This book gives a comprehensive account of the formulation and computational treatment of basic geometrically linear models in 1D. To set the stage, it assembles some preliminaries regarding necessary modelling, computational and mathematical tools. Thereafter, the remaining parts are concerned with the actual catalogue of computational material models. To this end, after starting out with elasticity as a reference, further 15 different basic variants of material models (5 x each of {visco...

This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics.The first part of the book discusses the basic numerical methods. The second part concentrates on simulation of classical and quantum systems. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method...

Since its conception in the 1960s, string theory has been hailed as one of the most promising routes we have to unify quantum mechanics and general relativity. This book provides a concise introduction to string theory explaining central concepts, mathematical tools and covering recent developments in physics including compactifications and gauge/string dualities. With string theory being a multidisciplinary field interfacing with high energy physics, mathematics and quantum field theory, ...

This book develops and applies a theory of the ambient metric in conformal geometry. This is a Lorentz metric in n+2 dimensions that encodes a conformal class of metrics in n dimensions. The ambient metric has an alternate incarnation as the Poincaré metric, a metric in n+1 dimensions having the conformal manifold as its conformal infinity. In this realization, the construction has played a central role in the AdS/CFT correspondence in physics.

This textbook presents basic numerical methods and applies them to a large variety of physical models in multiple computer experiments. Classical algorithms and more recent methods are explained. Partial differential equations are treated generally comparing important methods, and equations of motion are solved by a large number of simple as well as more sophisticated methods. Several modern algorithms for quantum wavepacket motion are compared. The first part of the book discusses the bas...

Condensed matter systems where interactions are strong are inherently difficult to analyze theoretically. The situation is particularly interesting in low-dimensional systems, where quantum fluctuations play a crucial role. Here, the development of non-perturbative methods and the study of integrable field theory have facilitated the understanding of the behavior of many quasi one- and two-dimensional strongly correlated systems. In view of the same rapid development that has taken place f...

Over the past few decades the powerful methods of statistical physics and Euclidean quantum field theory have moved closer together, with common tools based on the use of path integrals. The interpretation of Euclidean field theories as particular systems of statistical physics has opened up new avenues for understanding strongly coupled quantum systems or quantum field theories at zero or finite temperatures.Accordingly, the first chapters of this book contain a self-contained int...

This book reviews the construction of elementary systems living in de Sitter (dS) spacetime, in both the classical and quantum senses. Field theories on dS spacetime are among the most studied mathematical models of the Universe, whether for its earlier period (inflationary phase) or for its current phase of expansion acceleration (dark energy or cosmological constant). Classical elementary systems are Hamiltonian phase spaces, which are associated with co-adjoint orbits of the relativity ...

This book takes a pedagogical approach to explaining quantum gravity, supersymmetry and string theory in a coherent way. It is aimed at graduate students and researchers in quantum field theory and high-energy physics.The first part of the book introduces quantum gravity, without requiring previous knowledge of general relativity (GR). The necessary geometrical aspects are derived afresh leading to explicit general Lagrangians for gravity, including that of general relativity. The ...

The goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice. This book supersedes the author’s previous Springer book “Evaluating Feynman Integrals” and its textbook version “Feynman Integral Calculus.” Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods an...

This book provides the first graduate-level, self-contained introduction to recent developments that lead to the formulation of the configuration-interaction approach for open quantum systems, the Gamow shell model, which provides a unitary description of quantum many-body system in different regimes of binding, and enables the unification in the description of nuclear structure and reactions. The Gamow shell model extends and generalizes the phenomenologically successful nuclear shell mod...

This volume of the CRM Conference Series is based on a carefully refereed selection of contributions presented at the "11th International Symposium on Quantum Theory and Symmetries", held in Montréal, Canada from July 1-5, 2019. The main objective of the meeting was to share and make accessible new research and recent results in several branches of Theoretical and Mathematical Physics, including Algebraic Methods, Condensed Matter Physics, Cosmology and Gravitation, Integrability, Non-pert...