Search results for: renormalization-of-quantum-field-theories-with-non-linear-field-transformations

Renormalization of Quantum Field Theories with Non linear Field Transformations

Author : Peter Breitenlohner
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The characteristic feature of many models for field theories based on concepts of differential geometry is their nonlinearity. In this book a systematic exposition of nonlinear transformations in quantum field theory is given. The book starts with a short account of the renormalization theory with examples which can be handled successfully in four space-time dimensions. The second part is devoted to nonlinear sigma-models and their constructions in two dimensions. In the final section geometrical and cohomological methods and the relations to string theory are treated. This book is an important contribution towards rigorous definitions, and the mastering of nonlinear reparametrizations in agreement with the principles of quantum field theory will help to deal with anomalies, geometry and the like consistently and thus to understand better their implications for physics. The collection of papers addresses researchers and graduate students as well and will stimulate further work on the foundations of quantum field theory.

Renormalization of Quantum Field Theories with Non linear Field Transformations

Author : Peter Breitenlohner
File Size : 38.22 MB
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The characteristic feature of many models for field theories based on concepts of differential geometry is their nonlinearity. In this book a systematic exposition of nonlinear transformations in quantum field theory is given. The book starts with a short account of the renormalization theory with examples which can be handled successfully in four space-time dimensions. The second part is devoted to nonlinear sigma-models and their constructions in two dimensions. In the final section geometrical and cohomological methods and the relations to string theory are treated. This book is an important contribution towards rigorous definitions, and the mastering of nonlinear reparametrizations in agreement with the principles of quantum field theory will help to deal with anomalies, geometry and the like consistently and thus to understand better their implications for physics. The collection of papers addresses researchers and graduate students as well and will stimulate further work on the foundations of quantum field theory.

Renormalization of Quantum Field Theories with Non linear Field Transformations

Author : Peter Breitenlohner
File Size : 59.35 MB
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The characteristic feature of many models for field theories based on concepts of differential geometry is their nonlinearity. In this book a systematic exposition of nonlinear transformations in quantum field theory is given. The book starts with a short account of the renormalization theory with examples which can be handled successfully in four space-time dimensions. The second part is devoted to nonlinear sigma-models and their constructions in two dimensions. In the final section geometrical and cohomological methods and the relations to string theory are treated. This book is an important contribution towards rigorous definitions, and the mastering of nonlinear reparametrizations in agreement with the principles of quantum field theory will help to deal with anomalies, geometry and the like consistently and thus to understand better their implications for physics. The collection of papers addresses researchers and graduate students as well and will stimulate further work on the foundations of quantum field theory.

High Energy Physics Index

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Quantum Non linear Sigma Models

Author : Sergei V. Ketov
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Offers a systematic presentation of the modern quantum field theory of non-linear sigma-models. These models are very popular in theoretical high energy physics, string theory, and statistical physics. The geometric and quantum renormalization properties of the most general non-linear sigma-models are considered in detail within the framework of quantum perturbation theory. The main applications to be considered in the book can be found in string theory, conformal field theory, and general relativity.

Nuclear Science Abstracts

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ERDA Energy Research Abstracts

Author : United States. Energy Research and Development Administration
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Quantum Field Theory

Author : Peter Breitenlohner
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On the occasion of W. Zimmermann's 70th birthday some eminent scientists gave review talks in honor of one of the great masters of quantum field theory. It was decided to write them up and publish them in this book, together with reprints of some seminal papers of the laureate. Thus, this volume deepens our understanding of anomalies, algebraic renormalization theory, axiomatic field theory and of much more while illuminating the past and present state of affairs and pointing to interesting problems for future research.

Quantum Field Theory and Critical Phenomena

Author : Jean Zinn-Justin
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Introduced as a quantum extension of Maxwell's classical theory, quantum electrodynamics has been the first example of a Quantum Field Theory (QFT). Eventually, QFT has become the framework for the discussion of all fundamental interactions at the microscopic scale except, possibly, gravity. More surprisingly, it has also provided a framework for the understanding of second order phase transitions in statistical mechanics. As this work illustrates, QFT is the natural framework for the discussion of most systems involving an infinite number of degrees of freedom with local couplings. These systems range from cold Bose gases at the condensation temperature (about ten nanokelvin) to conventional phase transitions (from a few degrees to several hundred) and high energy particle physics up to a TeV, altogether more than twenty orders of magnitude in the energy scale. Therefore, this text sets out to present a work in which the strong formal relations between particle physics and the theory of critical phenomena are systematically emphasized. This option explains some of the choices made in the presentation. A formulation in terms of field integrals has been adopted to study the properties of QFT. The language of partition and correlation functions has been used throughout, even in applications of QFT to particle physics. Renormalization and renormalization group properties are systematically discussed. The notion of effective field theory and the emergence of renormalisable theories are described. The consequences for fine tuning and triviality issue are emphasized. This fifth edition has been updated and fully revised, e.g. in particle physics with progress in neutrino physics and the discovery of the Higgs boson. The presentation has been made more homogeneous througout the volume, and emphasis has been put on the notion of effective field theory and discussion of the emergence of renormalisable theories.

Random Walks Critical Phenomena and Triviality in Quantum Field Theory

Author : Roberto Fernandez
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Simple random walks - or equivalently, sums of independent random vari ables - have long been a standard topic of probability theory and mathemat ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the results obtained by random-walk methods are the proof of triviality of the cp4 quantum field theo ryin space-time dimension d (::::) 4, and the proof of mean-field critical behavior for cp4 and Ising models in space dimension d (::::) 4. The principal goal of the present monograph is to present a detailed review of these developments. It is supplemented by a brief excursion to the theory of random surfaces and various applications thereof. This book has grown out of research carried out by the authors mainly from 1982 until the middle of 1985. Our original intention was to write a research paper. However, the writing of such a paper turned out to be a very slow process, partly because of our geographical separation, partly because each of us was involved in other projects that may have appeared more urgent.