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Advances in Quantum Field Theory,Edited by Sergey Ketov. Published by InTech,Janeza Trdine 9 51000 Rijeka Croatia. Copyright 2012 InTech, All chapters are Open Access distributed under the Creative Commons Attribution 3 0. license which allows users to download copy and build upon published articles even for. commercial purposes as long as the author and publisher are properly credited which. ensures maximum dissemination and a wider impact of our publications After this work. has been published by InTech authors have the right to republish it in whole or part in. any publication of which they are the author and to make other personal use of the. work Any republication referencing or personal use of the work must explicitly identify. the original source, As for readers this license allows users to download copy and build upon published. chapters even for commercial purposes as long as the author and publisher are properly. credited which ensures maximum dissemination and a wider impact of our publications. Statements and opinions expressed in the chapters are these of the individual contributors. and not necessarily those of the editors or publisher No responsibility is accepted for the. accuracy of information contained in the published chapters The publisher assumes no. responsibility for any damage or injury to persons or property arising out of the use of any. materials instructions methods or ideas contained in the book. Publishing Process Manager Romana Vukelic,Technical Editor Teodora Smiljanic.

Cover Designer InTech Design Team,First published February 2012. Printed in Croatia, A free online edition of this book is available at www intechopen com. Additional hard copies can be obtained from orders intechweb org. Advances in Quantum Field Theory Edited by Sergey Ketov. ISBN 978 953 51 0035 5,Preface IX,Part 1 Quantization 1. Chapter 1 The Method of Unitary Clothing Transformations. in Quantum Field Theory Applications in the,Theory of Nuclear Forces and Reactions 3. A V Shebeko,Chapter 2 Ab Initio Hamiltonian Approach to.

Light Front Quantum Field Theory 31,James P Vary, Chapter 3 Quantizing with a Higher Time Derivative 51. Sergei V Ketov Genta Michiaki and Tsukasa Yumibayashi. Part 2 Applications to Low Energy Physics 73,Chapter 4 Electroweak Interactions in a Chiral. Effective Lagrangian for Nuclei 75,Brian D Serot and Xilin Zhang. Chapter 5 Ginzburg Landau Theory of Phase,Transitions in Compactified Spaces 103. C A Linhares A P C Malbouisson and I Roditi, Chapter 6 Quantum Field Theory of Exciton Correlations.

and Entanglement in Semiconductor Structures 125, M Erementchouk V Turkowski and Michael N Leuenberger. Part 3 Applications in Mathematics 153, Chapter 7 Quantum Field Theory and Knot Invariants 155. Chun Chung Hsieh,VI Contents,Chapter 8 Solution of a Linearized Model of. Heisenberg s Fundamental Equation 185,E Br ning and S Nagamachi. Chapter 9 Topological Singularity of Fermion Current. in Abelian Gauge Theory 215,Ai Dong Bao and Shi Shu Wu.

Quantum Field Theory was developed as the theory unifying Quantum Mechanics. and Relativistic Field Theory for the purpose of describing physics of elementary. particles Quantum Electrodynamics electro weak theory Quantum Chromodyna. mics and the Standard Model of elementary particles are all particular examples of. Quantum Field Theory which had great success in high energy physics At the same. time it was realized that a straightforward application of Quantum Field Theory to. Einstein gravity does not give a physically sensible quantum gravity theory because of. its nonrenormalizability, More recent applications of Quantum Field Theory are no longer limited to physics of. elementary particles They also include many successful applications to nuclear. physics condensed matter physics and pure mathematics At the same time the. formalism of Quantum Field Theory has to be further developed because of the new. challenges such as quantum gravity and quantization with higher derivatives strong. coupling and bound states computational techniques in quantum perturbation theory. and more rigorous mathematical foundations, In the first part of the book some recent progress in describing clothed particles by. unitary transformations together with their physical applications to nucleon scattering. and deuteron form factors are discussed A light front quantization in the Hamiltonian. approach and a quantization of Pais Uhlenbeck oscillator both in the Hamiltonian. approach and in the path integral approach are given. In the second part of the book some applications of Quantum Field Theory to low. energy physics are considered namely i electro weak interactions in a chiral. effective Lagrangian for nuclei ii Landau Ginsburg theory of phase transitions and. iii exciton correlators and quantum entanglement in semiconductors. In the third part of the book various relations between Quantum Field Theory and. mathematics are presented including knot invariants and Chern Simons Witten field. theory solutions to a linearized model of Heisenberg equation quantum anomalies. and Atiyah Singer index theorems, Though the book does not include all actual aspects of Quantum Field Theory and all. its recent advances it does include some of the relevant ones with a broad spectrum. of physical and mathematical applications, The book was made possible by the generous and professional assistance of Publishing. Process Manager Ms Romana Vukelic during all stages of editing I am very grateful. to her for pleasant collaboration,Prof Dr Sergey Ketov.

Tokyo Metropolitan University,Quantization,The Method of Unitary Clothing Transformations. in Quantum Field Theory Applications in the,Theory of Nuclear Forces and Reactions. A V Shebeko,Institute for Theoretical Physics, National Research Center Kharkov Institute of Physics Technology. 1 Introduction, In what follows we will show how one can realize the notion of clothed particles Greenberg. Schweber 1958 for eld theoretical treatments based upon the so called instant form of. relativistic dynamics formulated by Dirac Dirac 1949 In the context let us recall that the. notion points out a transparent way for including the so called cloud or persistent effects. in a system of interacting elds to be de nite mesons and nucleons A constructive. step see surveys Shebeko Shirokov 2000 2001 and refs therein is to express the. total eld Hamiltonian H and other operators of great physical meaning e g the Lorentz. boost generators and current density operators which depend initially on the creation and. destruction operators for the bare particles through a set of their clothed counterparts. It is achieved via unitary clothing transformations UCTs see article Korda et al 2007. in the Hilbert space H of meson nucleon states and we stress as before that each of such. transformations remains the Hamiltonian unchanged unlike other unitary transformation. methods Gl ckle M ller 1981 Kobayashi 1997 Okubo 1954 Stefanovich 2001 1 for. Hamiltonian based models In the course of the clothing procedure a large amount of. virtual processes associated in our case with the meson absorption emission the N N pair. annihilation production and other cloud effects turns out to be accumulated in the creation. destruction operators for the clothed particles The latter being the quasiparticles of the. method of UCTs must have the properties charges masses etc of physical observable. particles Such a bootstrap re ects the most signi cant distinction between the concepts of. clothed and bare particles, At the same time after Dirac any relativistic quantum theory may be so de ned that the.

generator of time translations Hamiltonian the generators of space translations linear. momentum space rotations angular momentum and Lorentz transformations boost. operator satisfy the well known commutations Basic ideas put forward by Dirac with his. front instant and point forms of the relativistic dynamics have been realized in many. relativistic quantum mechanical models In this context the survey Keister Polyzou 1991. being a remarkable introduction to a sub eld called the relativistic Hamiltonian dynamics. 1 Some speci c features of these methods are discussed in Shebeko Shirokov 2001 and Korda et al. VI Contents Chapter 8 Solution of a Linearized Model of Heisenberg s Fundamental Equation 185 E Br ning and S Nagamachi Chapter 9 Topological Singularity of Fermion Current in Abelian Gauge Theory 215 Ai Dong Bao and Shi Shu Wu

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