Author: Dieter Schuch Publisher: Springer ISBN: 3319655949 Category : Science Languages : en Pages : 261
Book Description
This book provides a unique survey displaying the power of Riccati equations to describe reversible and irreversible processes in physics and, in particular, quantum physics. Quantum mechanics is supposedly linear, invariant under time-reversal, conserving energy and, in contrast to classical theories, essentially based on the use of complex quantities. However, on a macroscopic level, processes apparently obey nonlinear irreversible evolution equations and dissipate energy. The Riccati equation, a nonlinear equation that can be linearized, has the potential to link these two worlds when applied to complex quantities. The nonlinearity can provide information about the phase-amplitude correlations of the complex quantities that cannot be obtained from the linearized form. As revealed in this wide ranging treatment, Riccati equations can also be found in many diverse fields of physics from Bose-Einstein-condensates to cosmology. The book will appeal to graduate students and theoretical physicists interested in a consistent mathematical description of physical laws.
Author: Anatoli? Karolevich Prikarpatski? Publisher: World Scientific ISBN: 9789812381644 Category : Science Languages : en Pages : 136
Book Description
Multi-photon excitation states of poly-atomic molecules undergoing a self-interaction via Kerr effect related processes are of great interest today. Their successful study must be both analytical and by means of modern quantum field theoretical tools. This book deals with these and related topics by developing modern quantum field theory methods for the analysis of radiative states in a nonlinear quantum-optical system. These lecture notes are ideally suited to graduate mathematical physics and physics students, but can also be of interest to mathematicians involved in applied physics problems, and physicists and chemists studying phenomena related with modern quantum-optical devices.
Author: Tony Hilton Royle Skyrme Publisher: World Scientific ISBN: 9810216467 Category : Science Languages : en Pages : 456
Book Description
The most important papers of Tony Hilton Royle Skyrme are collected in this volume which also includes commentaries by G Brown and other articles relating to the life and work of Tony Skryme, R Dalitz, E Witten and others. Skyrme's work was brilliant, profound and surprisingly useful. He provided an original solution to the problem of constructing fermions from bosons, formulating the topological soliton model of the nucleon. His two-parameter model of effective interactions in nuclei has yielded a remarkably accurate description of nuclear structure. His à-particle model of nuclei gave deep insights into the structure of important and complicated excited states.This volume is a unique collection of Tony Skyrme's work. It is a must for all physicists in the high energy, nuclear and mathematical physics community.
Author: Alexander G. Kyriakos Publisher: AKVY PRESS ISBN: 0980966744 Category : Quantum field theory Languages : en Pages : 164
Book Description
The author proposes a special nonlinear quantum field theory. In a linear approximation, this theory can be presented in the form of the Standard Model (SM) theory. The richer physical structure of this nonlinear theory makes it possible to exceed the limits of SM and remove its known incompleteness. We show that nonlinearity of the field is critical for the appearance of charges and masses of elementary particles, for confinement of quarks, and many other effects, whose description within the framework of SM causes difficulties. In this case, the mechanism of generation of masses is mathematically similar to Higgs's mechanism, but it is considerably simpler and does not include the additional particles. The proposed theory does not examine the theory of gravity, but reveals the mathematical similarity of the nonlinear field equations of both theories. The book is intended for undergraduate and graduate students studying the theory of elementary particles, as well as for specialists working in this field.
Author: P. Barut Publisher: Springer Science & Business Media ISBN: 9400998910 Category : Mathematics Languages : en Pages : 470
Book Description
This is the third Volume in a series of books devoted to the interdisciplinary area between mathematics and physics, all ema nating from the Advanced Study Institutes held in Istanbul in 1970, 1972 and 1977. We believe that physics and mathematics can develop best in harmony and in close communication and cooper ation with each other and are sometimes inseparable. With this goal in mind we tried to bring mathematicians and physicists together to talk and lecture to each other-this time in the area of nonlinear equations. The recent progress and surge of interest in nonlinear ordi nary and partial differential equations has been impressive. At the same time, novel and interesting physical applications mul tiply. There is a unifying element brought about by the same characteristic nonlinear behavior occurring in very widely differ ent physical situations, as in the case of "solitons," for exam ple. This Volume gives, we believe, a very good indication over all of this recent progress both in theory and applications, and over current research activity and problems. The 1977 Advanced Study Institute was sponsored by the NATO Scientific Affairs Division, The University of the Bosphorus and the Turkish Scientific and Technical Research Council. We are deeply grateful to these Institutions for their support, and to lecturers and participants for their hard work and enthusiasm which created an atmosphere of lively scientific discussions.
Author: Frederick W. Byron Publisher: Courier Corporation ISBN: 0486135063 Category : Science Languages : en Pages : 674
Book Description
Graduate-level text offers unified treatment of mathematics applicable to many branches of physics. Theory of vector spaces, analytic function theory, theory of integral equations, group theory, and more. Many problems. Bibliography.
Author: G. Giachetta Publisher: World Scientific ISBN: 9812838961 Category : Science Languages : en Pages : 393
Book Description
Contemporary quantum field theory is mainly developed as quantization of classical fields. Therefore, classical field theory and its BRST extension is the necessary step towards quantum field theory. This book aims to provide a complete mathematical foundation of Lagrangian classical field theory and its BRST extension for the purpose of quantization. Based on the standard geometric formulation of theory of nonlinear differential operators, Lagrangian field theory is treated in a very general setting. Reducible degenerate Lagrangian theories of even and odd fields on an arbitrary smooth manifold are considered. The second Noether theorems generalized to these theories and formulated in the homology terms provide the strict mathematical formulation of BRST extended classical field theory. The most physically relevant field theories OCo gauge theory on principal bundles, gravitation theory on natural bundles, theory of spinor fields and topological field theory OCo are presented in a complete way. This book is designed for theoreticians and mathematical physicists specializing in field theory. The authors have tried throughout to provide the necessary mathematical background, thus making the exposition self-contained.
Author: Luigi Mangiarotti Publisher: World Scientific ISBN: 9814501409 Category : Science Languages : en Pages : 516
Book Description
Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models in field theory and mechanics. This book is an encyclopaedia of modern geometric methods in theoretical physics. It collects together the basic mathematical facts about various types of connections, and provides a detailed exposition of relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental fields. The authors have tried to give all the necessary mathematical background, thus making the book self-contained.This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.
Author: Maurice Jacob Publisher: World Scientific ISBN: 9814518891 Category : Science Languages : en Pages : 526
Book Description
Contents: Extended Systems in Field Theory :Introduction (J-L Gervais and A Neveu)Vortices and Quark Confinement in Non-Abelian Gauge Theories (S Mandelstam)Magnetic and Electric Confinement of Quarks (Y Nambu)Examples of Four-Dimensional Soliton Solutions and Abnormal Nuclear States (T D Lee)Classical Solution in the Massive Thirring Model (S-J Chang)Semiclassical Quantization Methods in Field Theory (A Neveu)The Quantum Theory of Solitons and Other Non-Linear Classical Waves (R Jackiw)Collective Coordinate Method for Quantization of Extended Systems (J-L Gervais, A Jevicki and B Sakita)Quantum Expansion of Soliton Solutions (N H Christ)Hartree-Type Approximation Applied to a ϕ4 Field Theory (S-J Chang)Soliton Operators for the Quantized Sine–Gordon Equation (S Mandelstam)Classical Aspects and Fluctuation-Behaviour of Two Dimensional Models in Statistical Mechanics and Many Body Physics (B Schroer)Quarks on a Lattice, or, the Colored String Model (K G Wilson)New Ideas about Confinement (L Susskind and J Kogut)Gauge Fields on a Lattice (C Itzykson)Non-Perturbative Aspects in Quantum Field Theory:Self-Dual Solutions to Euclidean Yang–Mills Equations (E Corrigan)An Introduction to the Twistor Programme (J Madore, J L Richard and R Stora)Collective Coordinates with Non-Trivial Dynamics (J-L Gervais)A Theory of the Strong Interactions (D J Gross)Magneticmonopoles (D Olive)Dynamical and Topological Considerations on Quark Confinement (F Englert and P Windey)Difficulties in Fixing the Gauge in Non-Abelian Gauge Theories (S Sciuto)Indeterminate-Mass Particles (B M Mccoy and T T Wu)Duality for Discrete Lattice Gauge Fields (C Itzykson)Large Order Estimates in Perturbation Theory (J Zinn-Justin)The Borel Transform and the Renormalization Group (G Parisi)Planar Diagrams (E Brezin)Exact S-Matrices and Form Factors in 1 + 1 Dimensional Field Theoretic Models with Soliton Behaviour (M Karowski)Topology and Higher Symmetries of the Two-Dimensional Nonlinear σ Model (A D'adda, M Luscher and P Di Vecchia)Two-Dimensional Yang–Mills Theory in the Leading 1/N Expansion (T T Wu)Superfluidity and the Two-Dimensional XY Model' (D R Nelson)Bosonized Fermions in Three Dimensions (A Luther)Symmetry and Topology Concepts for Spin Glasses and Other Glasses (G Toulouse)Common Trends in Particle and Condensed Matter Physics:Introduction to Localization(D J Thouless)Conductivity Scaling and Localization(E Abrahams)Disordered Electronic System as a Model of Interacting Matrices(F Wegner)Status Report on Spin Glasses (Not Included in this Report)(S Kirkpatrick)Mean Field Theory for Spin Glasses(G Parisi)The Random Energy Model(B Derrida)Towards a Mean Field Theory of Spin Glasses: the Tap Route Revisited (C De Dominicis)On the Connection Between Spin Glasses and Gauge Field Theories(G Toulouse, J Vannimenus)Monte Carlo Simulations of Lattice Gauge Theories(C Rebbi)Large Dimension Expansions and Transition Patterns in Lattice Gauge Theories(J-M Drouffe)Progress in Lattice Gauge Theory(J B Kogut)Phase Structure of the Z(2) Gauge and Matter Theory(D Horn)General Introduction to Confinement(S Mandelstam)A Simple Picture of the Weak-to-Strong Coupling Transition in Quantum Chromodynamics(C G Callan Jr.)Quantum Fluctuations in a Multiinstanton Background(B A Berg)Some Comments on the Crossover Between Strong and Weak Coupling in Su(2) Pure Yang–Mills Theory(J Frohlich)String Dynamics in QCD (J-L Gervais, A Neveu)Dual Models and Strings: The Critical Dimension(C B Thorn: )Duality and Finite Size Effects in Six Vertex Models(C.B. Thorn: )Scaling at a Bifurcation Point(M Nauenberg, D Scalapino)Some Implications of a Cosmological Phase Transition(T W B Kibble) Readership: Graduate students and researchers in particle physics andcondensed matter physics.
Author: Dieter Schuch
Author: Anatoli? Karolevich Prikarpatski?
Author: Tony Hilton Royle Skyrme
Author: Alexander G. Kyriakos
Author: P. Barut
Author: Frederick W. Byron
Author: M. S. Birman
Author: G. Giachetta
Author: Luigi Mangiarotti
Author: Maurice Jacob