thermal quantum field theory

Thermal field theory is the study of quantum field theory at non-zero temperature. This proceedings introduces both retrospect and prospect for various aspects of thermal field theory as well as their extensive applications to condensed matter physics, high energy physics, cosmology, nuclear physics etc. Also included are speeches memorizing the recently lamented Professor Hiroomi Umezawa, a leading physicist in thermal field theory, by his former students and colleagues.

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Theories of quantum fields at non-zero temperature have been steadily developed for well over a decade. In 1988, as a result of the increased demand for communication among theorists working in different fields ranging from condensed matter physics to high energy physics and astrophysics, the first international meeting was organized (the proceedings of which have been published in Physica A 158, 1989) . This 2nd workshop covers similar fields, namely equilibrium and non-equilibrium statistical physics, quantum optics, high-temperature gauge-field theories, string theories, statistical theories of gravitation and cosmology. The resulting proceedings reflect the progress made in the respective fields, identify the major common problems and suggest possible directions for their solutions.

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This work begins by distinguishing the difference between quantum mechanics and quantum field theory. It then attempts to extend field theory by adding a thermal degree of freedom to phenomena occurring within a vacuum. The resulting quantum field theory is called Thermo Field Dynamics (TFD).

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Tanguy Altherr was a Fellow in the Theory Division at CERN, on leave from LAPP (CNRS) Annency. At the time of his accidental death in July 1994, he was only 31. A meeting was organized at CERN, covering the various aspects of his scientific interests: thermal field theory and its applications to hot or dense media, neural networks and its applications to high energy data analysis. Speakers were among his closest collaborators and friends.

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The AdS/CFT correspondence is a powerful tool in studying strongly coupled phenomena in gauge field theories, using results from a weakly coupled gravity background studied in the realm of string theory. AdS/CFT was first successfully applied to the study of phenomena such as the quark-gluon plasma produced in heavy ions collisions. Soon it was realized that its applicability can be extended, in a more phenomenological approach, to condensed matter systems and to systems described by fluid dynamics.

 The set of tutorial reviews in this volume is intended as an introduction to and survey of the principle of the AdS/CFT correspondence in its field/string theoretic formulation, its applicability to holographic QCD and to heavy ions collisions, and to give a first account of processes in fluid dynamics and condensed matter physics, which can be studied with the use of this principle.

 Written by leading researchers in the field and cast into the form of a high-level but approachable multi-author textbook, this volume will be of benefit to all postgraduate students, and newcomers from neighboring disciplines wishing to find a comprehensive guide for their future research.

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This text introduces the theoretical framework for describing the quark-gluon plasma, an important new state of matter. The first part of the book is a self-contained introduction to relativistic thermal field theory. Topics include the path integral approach, the real and imaginary time formalisms, fermion fields and gauge fields at finite temperature. The author illustrates useful techniques such as the evaluation of frequency sums and the use of cutting rules. The second part of the book is devoted to recent developments, and gives a detailed account of collective excitations (bosonic and fermionic), showing how they give rise to energy scales that imply a reorganization of perturbation theory. The author also explains the relation with kinetic theory. He works out in detail applications to processes that occur in heavy ion collisions and in astrophysics. Each chapter ends with exercises and a guide to the literature. Graduate students and researchers in nuclear, particle, and astrophysics will benefit from this book.

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This monograph presents recent developments in quantum field theory at finite temperature. By using Lie groups, ideas from thermal theory are considered with concepts of symmetry, allowing for applications not only to quantum field theory but also to transport theory, quantum optics and statistical mechanics. This includes an analysis of geometrical and topological aspects of spatially confined systems with applications to the Casimir effect, superconductivity and phase transitions. Finally, some developments in open systems are also considered. The book provides a unified picture of the fundamental aspects in thermal quantum field theory and their applications, and is important to the field as a result, since it combines several diverse ideas that lead to a better understanding of different areas of physics.

Contents: General Principles: Elements of Thermodynamics; Elements of Statistical Mechanics; Partition Function and Path Integral; Zero Temperature Interacting Fields; Thermal Fields: Thermofield Dynamics: Kinematical Symmetry Algebraic Basis; Thermal Oscillators: Bosons and Fermions; Thermal Poincaré and Galilei Groups; Thermal Propagator; Scattering Process at Finite Temperature; Topics on Renormalization Theory; Ward-Takahashi Relations and Gauge Symmetry; Applications to Quantum Optics: Thermalized States of a Field Mode; Nonclassical Properties of Thermal Quantum States; SU(2) and SU(1,1) Systems: Entanglement; Compactified Fields: Compactified Fields; Casimir Effect for the Electromagnetic Field; Casimir Effect for Fermions; Compactified 4 Theory; Phase Transitions in Confined Systems: Application to Superconducting Films; Second-Order Phase Transition in Wires and Grains; First-Order Phase Transitions in Confined Systems; Applications to Open Systems: Thermo-Algebras in Phase Space: Quantum and Classical Systems; Real-Time Method for Nonequilibrium Quantum Mechanics; Dressed and Bare State Approaches to the Thermalization Process.

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