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Unifying a range of topics that are currently scattered throughout the literature, this book offers a unique and definitive review of mathematical aspects of quantization and quantum field theory. The authors present both basic and more advanced topics of quantum field theory in a mathematically consistent way, focusing on canonical commutation and anti-commutation relations. They begin with a discussion of the mathematical structures underlying free bosonic or fermionic fields, like tensors, algebras, Fock spaces, and CCR and CAR representations (including their symplectic and orthogonal invariance). Applications of these topics to physical problems are discussed in later chapters. Although most of the book is devoted to free quantum fields, it also contains an exposition of two important aspects of interacting fields: diagrammatics and the Euclidean approach to constructive quantum field theory. With its in-depth coverage, this text is essential reading for graduate students and researchers in departments of mathematics and physics.

This volume summarizes the many alternatives and extensions to Einstein's General Theory of Relativity, and shows how symmetry principles can be applied to identify physically viable models. The first part of the book establishes the foundations of classical field theory, providing an introduction to symmetry groups and the Noether theorems. A quick overview of general relativity is provided, including discussion of its successes and shortcomings, then several theories of gravity are presented and their main features are summarized. In the second part, the 'Noether Symmetry Approach' is applied to theories of gravity to identify those which contain symmetries. In the third part of the book these selected models are tested through comparison with the latest experiments and observations. This constrains the free parameters in the selected models to fit the current data, demonstrating a useful approach that will allow researchers to construct and constrain modified gravity models for further applications.

"Coherence is highly valued in law. It is especially sought after in investor-state dispute settlement, where charges of incoherence in arbitral awards have long been raised by states and scholars. Yet coherence is a largely underexplored notion in international law. Often, coherence is treated as a mere ideal to strive towards or simply as a different way to describe the legal consistency of judicial outcomes. This book takes a different approach. It views coherence as an independent concept having two dimensions: a substantive and a methodological one. Both are critical for legal reasoning by international courts and tribunals, including by investor-state tribunals, and the book illustrates through several case studies some of the ways this conclusion is borne out in practice. A fuller understanding of coherence in international law has implications for the way we should understand the concept of law, the practice of legal reasoning, and judicial professional ethics"--

This book was originally published in 2006. Moonshine forms a way of explaining the mysterious connection between the monster finite group and modular functions from classical number theory. The theory has evolved to describe the relationship between finite groups, modular forms and vertex operator algebras. Moonshine Beyond the Monster describes the general theory of Moonshine and its underlying concepts, emphasising the interconnections between mathematics and mathematical physics. Written in a clear and pedagogical style, this book is ideal for graduate students and researchers working in areas such as conformal field theory, string theory, algebra, number theory, geometry and functional analysis. Containing over a hundred exercises, it is also a suitable textbook for graduate courses on Moonshine and as supplementary reading for courses on conformal field theory and string theory.

Providing a new perspective on quantum field theory, this book gives a pedagogical and up-to-date exposition of non-perturbative methods in relativistic quantum field theory and introduces the reader to modern research work in theoretical physics. It describes in detail non-perturbative methods in quantum field theory, and explores two- dimensional and four- dimensional gauge dynamics using those methods. The book concludes with a summary emphasizing the interplay between two- and four- dimensional gauge theories. Aimed at graduate students and researchers, this book covers topics from two-dimensional conformal symmetry, affine Lie algebras, solitons, integrable models, bosonization, and 't Hooft model, to four-dimensional conformal invariance, integrability, large N expansion, Skyrme model, monopoles and instantons. Applications, first to simple field theories and gauge dynamics in two dimensions, and then to gauge theories in four dimensions and quantum chromodynamics (QCD) in particular, are thoroughly described.

This book provides a coherent exposition of the techniques underlying these calculations.

This book develops the basic formalism and theoretical techniques for studying relativistic quantum field theory at high temperature and density. Specific physical theories treated include QED, QCD, electroweak theory, and effective nuclear field theories of hadronic and nuclear matter. Topics covered include: functional integral representation of the partition function, diagrammatic expansions, linear response theory, screening and plasma oscillations, spontaneous symmetry breaking, Goldstone theorem, resummation and hard thermal loops, lattice gauge theory, phase transitions, nucleation theory, quark-gluon plasma, and color superconductivity. Applications to astrophysics and cosmology cover white dwarf and neutron stars, neutrino emissivity, baryon number violation in the early universe, and cosmological phase transitions. Applications to relativistic nucleus-nucleus collisions are also included. The book is written for theorists in elementary particle physics, nuclear physics, astrophysics, and cosmology. Released initially in 2006, this title has been reissued as an Open Access publication on Cambridge Core.

This 2002 book introduces the quantum theory of gauge fields. Emphasis is placed on four non-perturbative methods: path integrals, lattice gauge theories, the 1/N expansion, and reduced matrix models, all of which have important contemporary applications. Written as a textbook, it assumes a knowledge of quantum mechanics and elements of perturbation theory, while many relevant concepts are pedagogically introduced at a basic level in the first half of the book. The second half comprehensively covers large-N Yang-Mills theory. The book uses an approach to gauge theories based on path-dependent phase factors known as the Wilson loops, and contains problems with detailed solutions to aid understanding. Suitable for advanced graduate courses in quantum field theory, the book will also be of interest to researchers in high energy theory and condensed matter physics as a survey of recent developments in gauge theory.