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"This book is offer a systematic account of the role of language in the development and interpretation of physics. An historical-conceptual analysis of the co-evolution of mathematical and physical concepts leads to the classical/quatum interface. Bohrian orthodoxy stresses the indispensability of classical concepts and the functional role of mathematics. This book analyses ways of extending, and then going beyond this orthodoxy orthodoxy. Finally, the book analyzes how a revised interpretation of physics impacts on basic philosophical issues, conceptual revolutions, realism, and reductionism."

"Classical solutions play an important role in quantum field theory, high-energy physics and cosmology. Real-time soliton solutions give rise to particles, such as magnetic monopoles, and extended structures, such as domain walls and cosmic strings, that have implications for early universe cosmology. Imaginary-time Euclidean instantons are responsible for important non perturbative effects, while Euclidean bounce solutions govern transitions between metastable states. Written for advanced graduate students and researchers in elementary particle physics, cosmology and related fields, this book brings the reader up to the level of current research in the field. The first half of the book discusses the most important classes of solitons: kinks, vortices and magnetic monopoles. The cosmological and observational constraints on these are covered, as are more formal aspects, including BPS solitons and their connection with supersymmetry. The second half is devoted to Euclidean solutions, with particular emphasis on Yang–Mills instantons and on bounce solutions."

"Since the previous fourth edition has received quite a positive response from students as well as teachers, we have decided to extend the contents and improve some chapters for pedagogical reasons. In particular, we have rewritten Chap. 33, which is now entitled, “Classical Geometric Phases: Foucault and Euler.” However, most importantly, we have added a new chapter, Chap. 38: “The Usefulness of Lie Brackets: From Classical and Quantum Mechanics to Quantum Electrodynamics.” We emphasize the usefulness of the Lie brackets in classical and quantum mechanics up to quantum electrodynamics. Especially many dynamical systems with (gauge) constraints can equally be treated in the time development with noncanonical variables and Hamiltonians. This is convincingly demonstrated for the electron propagation function in a constant magnetic field in three and four dimensions. We also have attempted to remove the inevitable typos from the text and formulas."