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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"--