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“…Classical solutions play an important role in quantum field theory, high energy physics and cosmology. …”
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“…Based on classical transport theory, we present a general set of covariant equations describing the dynamics of mean fields and their statistical fluctuations in a non-Abelian plasma in or out-of-equilibrium. …”
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“…In recent years an increasing number of papers have attempted to mimic or supplant quantum field theory in discussions of issues related to gravity by the tools and through the perspective of quantum information theory, often in the context of alternative quantum theories. …”
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“…A canonical quantization approach to classical field theory, this text includes an introduction to differential geometry, the theory of Lie groups, and covariant Hamiltonian formulation of field theory. 1988 edition.…”
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“…Gauss created the theory of binary quadratic forms in "Disquisitiones Arithmeticae" and Kummer invented ideals and the theory of cyclotomic fields in his attempt to prove Fermat's Last Theorem These were the starting points for the theory of algebraic numbers, developed in the classical papers of Dedekind, Dirichlet, Eisenstein, Hermite and many others This theory, enriched with more recent contributions, is of basic importance in the study of diophantine equations and arithmetic algebraic geometry, including methods in cryptography This book has a clear and thorough exposition of the classical theory of algebraic numbers, and contains a large number of exercises as well as worked out numerical examples The Introduction is a recapitulation of results about principal ideal domains, unique factorization domains and commutative fields Part One is devoted to residue classes and quadratic residues In Part Two one finds the study of algebraic integers, ideals, units, class numbers, the theory of decomposition, inertia and ramification of ideals Part Three is devoted to Kummer's theory of cyclomatic fields, and includes Bernoulli numbers and the proof of Fermat's Last Theorem for regular prime exponents Finally, in Part Four, the emphasis is on analytical methods and it includes Dinchlet's Theorem on primes in arithmetic progressions, the theorem of Chebotarev and class number formulas A careful study of this book will provide a solid background to the learning of more recent topics…”
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“…The book begins with a brief reminder of basic classical field theories, electrodynamics and general relativity, as well as their symmetry properties, and proceeds with the principles of quantisation following Feynman's path integral approach. …”
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“…Written by a physicist for physicists, the book is designed to help readers develop analytical skills related to classical and quantum fields at the non-relativistic level, and think about the concepts and theory through numerous problems. …”
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“…Microcontinuum field theories constitute an extension of classical field theories -- of elastic bodies, deformations, electromagnetism, and the like -- to microscopic spaces and short time scales. …”
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“…The dynamics of electrons and quarks is described by the Standard Model of particle physics, which is based on quantum field theories. The general framework of quantum field theories is described in this book. …”
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“…Conformal field theory is an elegant and powerful theory in the field of high energy physics and statistics. …”
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