Download or read book Fluctuating Paths And Fields Festschrift Dedicated To Hagen Kleinert On The Occasion Of His 60th Birthday written by Michael Bachmann and published by World Scientific. This book was released on 2001-06-04 with total page 874 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers the following fields: path integrals, quantum field theory, variational perturbation theory, phase transitions and critical phenomena, topological defects, strings and membranes, gravitation and cosmology.
Download or read book Complex Nonlinearity written by Vladimir G. Ivancevic and published by Springer Science & Business Media. This book was released on 2008-05-31 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.
Download or read book Applied Differential Geometry written by Vladimir G. Ivancevic and published by World Scientific. This book was released on 2007 with total page 1346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level monographic textbook treats applied differential geometry from a modern scientific perspective. Co-authored by the originator of the world's leading human motion simulator ? ?Human Biodynamics Engine?, a complex, 264-DOF bio-mechanical system, modeled by differential-geometric tools ? this is the first book that combines modern differential geometry with a wide spectrum of applications, from modern mechanics and physics, via nonlinear control, to biology and human sciences. The book is designed for a two-semester course, which gives mathematicians a variety of applications for their theory and physicists, as well as other scientists and engineers, a strong theory underlying their models.
Download or read book Geometrical Dynamics of Complex Systems written by Vladimir G. Ivancevic and published by Springer Science & Business Media. This book was released on 2006-09-10 with total page 842 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometrical Dynamics of Complex Systems is a graduate?level monographic textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical dynamicsofcomplexsystemsofvariousnatures. By?complexsystems?,inthis book are meant high?dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a uni?ed geometrical - proachtodynamicsofcomplexsystemsofvariouskinds:engineering,physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these multi?input multi?output (MIMO) systems have something in common: the underlying physics. However, instead of dealing with the pop- 1 ular ?soft complexity philosophy?, we rather propose a rigorous geometrical and topological approach. We believe that our rigorous approach has much greater predictive power than the soft one. We argue that science and te- nology is all about prediction and control. Observation, understanding and explanation are important in education at undergraduate level, but after that it should be all prediction and control. The main objective of this book is to show that high?dimensional nonlinear systems and processes of ?real life? can be modelled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. It is well?known that linear systems, which are completely predictable and controllable by de?nition ? live only in Euclidean spaces (of various - mensions). They are as simple as possible, mathematically elegant and fully elaborated from either scienti?c or engineering side. However, in nature, no- ing is linear. In reality, everything has a certain degree of nonlinearity, which means: unpredictability, with subsequent uncontrollability.
Download or read book Particles And Quantum Fields written by Hagen Kleinert and published by World Scientific. This book was released on 2016-05-30 with total page 1628 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory book on elementary particles and their interactions. It starts out with many-body Schrödinger theory and second quantization and leads, via its generalization, to relativistic fields of various spins and to gravity. The text begins with the best known quantum field theory so far, the quantum electrodynamics of photon and electrons (QED). It continues by developing the theory of strong interactions between the elementary constituents of matter (quarks). This is possible due to the property called asymptotic freedom. On the way one has to tackle the problem of removing various infinities by renormalization. The divergent sums of infinitely many diagrams are performed with the renormalization group or by variational perturbation theory (VPT). The latter is an outcome of the Feynman-Kleinert variational approach to path integrals discussed in two earlier books of the author, one representing a comprehensive treatise on path integrals, the other dealing with critial phenomena. Unlike ordinary perturbation theory, VPT produces uniformly convergent series which are valid from weak to strong couplings, where they describe critical phenomena.The present book develops the theory of effective actions which allow to treat quantum phenomena with classical formalism. For example, it derives the observed anomalous power laws of strongly interacting theories from an extremum of the action. Their fluctuations are not based on Gaussian distributions, as in the perturbative treatment of quantum field theories, or in asymptotically-free theories, but on deviations from the average which are much larger and which obey power-like distributions.Exactly solvable models are discussed and their physical properties are compared with those derived from general methods. In the last chapter we discuss the problem of quantizing the classical theory of gravity.
Download or read book Physics of the Magnetosphere written by R.L. Carovillano and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 693 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based upon the proceedings of the Summer Institute, Physics of the Magnetosphere, held on the Boston College campus, lune 19-28, 1967. The pro gram consisted of invited speakers selected by the Editors. An attempt was made to provide comprehensive treatment of all topics of primary relevance to magneto spheric physics, but, of course, some areas received greater coverage than others. The first portion of the conference consisted of tutoriallectures, four each, by five distinguished scientists, and these are presented in Part I of the monograph. The artides appearing in Part I were prepared by the Editors from tapes of the actual lectures. Preliminary manuscripts were prepared and each tutoriallecturer was given the opportunity to make changes or improvements that were incorporated into the final manuscript. H. R. Radoski prepared the lectures of Professor Helliwell; 1. F. McClay prepared the lectures of Professor Dessler and the first two of Professor Dungey; and the remaining lectures of Professors Dungey, Parker, and Van Allen were prepared by me. An effort was made for the most part to write each manuscript in the style of the lectures, but the incongruities of spoken English and the number of scribes in the kitchen undoubtedly limited our success. Everyone knows that English is written far better than it is spoken, although for some reason the spoken word is more dear.
Download or read book Computational Mind A Complex Dynamics Perspective written by Vladimir G. Ivancevic and published by Springer Science & Business Media. This book was released on 2007-06-12 with total page 698 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate–level monographic textbook in the field of Computational Intelligence. It presents a modern dynamical theory of the computational mind, combining cognitive psychology, artificial and computational intelligence, and chaos theory with quantum consciousness and computation. The book introduces to human and computational mind, comparing and contrasting main themes of cognitive psychology, artificial and computational intelligence.
Download or read book Quantum Leap From Dirac And Feynman Across The Universe To Human Body And Mind written by Vladimir G Ivancevic and published by World Scientific. This book was released on 2008-10-09 with total page 855 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique 21st-century monograph that reveals a basic, yet deep understanding of the universe, as well as the human mind and body — all from the perspective of quantum mechanics and quantum field theory.This book starts with both non-mathematical and mathematical preliminaries. It presents the basics of both non-relativistic and relativistic quantum mechanics, and introduces Feynman path integrals and their application to quantum fields and string theory, as well as some non-quantum applications. It then describes the quantum universe in the form of loop quantum gravity and quantum cosmology. Lastly, the book turns to the human body and mind, applying quantum theory to electro-muscular stimulation and consciousness.It can be used as a graduate (or advanced undergraduate) textbook for a two-semester course in quantum physics and its modern applications. Some parts of the book can also be used by engineers, biologists, psychologists and computer scientists, as well as applied mathematicians, both in industry and academia.
Download or read book Cellular Molecular Mechanisms in Epigenetic Evolutionary Biology written by John Torday and published by Springer Nature. This book was released on 2020-02-13 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been no mechanistic explanation for evolutionary change consistent with phylogeny in the 150 years since the publication of ‘Origins’. As a result, progress in the field of evolutionary biology has stagnated, relying on descriptive observations and genetic associations rather testable scientific measures. This book illuminates the need for a larger evolutionary-based platform for biology. Like physics and chemistry, biology needs a central theory in order to frame the questions that arise, the way hypotheses are tested, and how to interpret the data in the context of a continuum.The reduction of biology to its self-referential, self-organized properties provides the opportunity to recognize the continuum from the Singularity/Big Bang to Consciousness based on cell-cell communication for homeostasis.
Download or read book Matter Particled written by Yuval Ne'eman and published by World Scientific. This book was released on 2006 with total page 895 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume contains a selection of more than 80 of Yuval Ne''eman''s papers, which represent his huge contribution to a large number of aspects of theoretical physics. The works span more than four decades, from unitary symmetry and quarks to questions of complexity in biological systems and evolution of scientific theories. In keeping with the major role Ne''eman has played in theoretical physics over the last 40 years, a collaboration of very distinguished scientists enthusiastically took part in this volume. Their commentary supplies a clear framework and background for appreciating Yuval Ne''eman''s significant discoveries and pioneering contributions. Contents: (Authors of Commentaries in Parentheses): SU(3), Quarks and Symmetry Breaking (Y Verbin); Algebraic Theory of Particle Physics and Spectrum Generating Algebras (N Cabibbo); Supersymmetry and Supergravity (R Kerner); Geometrization of Physics (T Regge); SU(2/1) Super-Unification of the Standard Model and Non Commutative Geometry (J Thierry-Mieg); Spinor Representations of GL ( N, P ) and Chromogravity (I Kirsch); Metric-Affine Gravity (F W Hehl); Strings, Branes and Other Extendons (Dj aijaiki); Various Topics in Astrophysics (J Bahcall); Foundations of Physics (A Botero); Philosophy and Sociology of Science: Evolution and History (J Rosen). Readership: Researchers in physics and mathematical physics, and scientists interested in history of physics and philosophy of science."
Download or read book Neuro Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling written by Vladimir G. Ivancevic and published by Springer. This book was released on 2007-04-11 with total page 738 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents a comprehensive introduction into both conceptual and rigorous brain and cognition modelling. It is devoted to understanding, prediction and control of the fundamental mechanisms of brain functioning. The reader will be provided with a scientific tool enabling him or her to perform a competitive research in brain and cognition modelling. This is a graduate–level monographic textbook.
Download or read book Path Integrals in Quantum Mechanics Statistics Polymer Physics and Financial Markets written by Hagen Kleinert and published by World Scientific Publishing Company. This book was released on 2004-03-05 with total page 1505 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third, significantly expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions. The powerful Feynman–Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals. Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders. Special attention is devoted to path integrals with topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern–Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect. The relevance of path integrals to financial markets is discussed, and improvements of the famous Black–Scholes formula for option prices are given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions. The author's other book on 'Critical Properties of Φ4 Theories' gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions. Request Inspection Copy
Download or read book Natural Biodynamics written by Vladimir G Ivancevic and published by World Scientific. This book was released on 2005-11-29 with total page 1036 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume is a graduate-level text in human biodynamics, written in the unified categorical language of modern differential geometry and topology. Combining mathematics, physics and robotics with human physiology, this is the first book that describes all levels of human biodynamics, from musculo-skeletal mechanics to the higher brain functions. The book develops and uses a variety of research methods, ranging from chaos theory and Haken's synergetics, through quantum mechanics, to nonlinear control and artificial intelligence, to provide the means to understand, predict and control the behavior of human-like systems in their full neuro-musculo-skeletal complexity. The applications of this unique scientific methodology range from prediction of human neuro-musculo-skeletal injuries to brain-like control of humanoid robots.
Download or read book Path Integrals in Quantum Mechanics Statistics Polymer Physics and Financial Markets written by Hagen Kleinert and published by World Scientific Publishing Company. This book was released on 2006-07-19 with total page 1592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth, expanded edition of the comprehensive textbook published in 1990 on the theory and applications of path integrals. It is the first book to explicitly solve path integrals of a wide variety of nontrivial quantum-mechanical systems, in particular the hydrogen atom. The solutions have become possible by two major advances. The first is a new euclidean path integral formula which increases the restricted range of applicability of Feynman's famous formula to include singular attractive 1/r and 1/r2 potentials. The second is a simple quantum equivalence principle governing the transformation of euclidean path integrals to spaces with curvature and torsion, which leads to time-sliced path integrals that are manifestly invariant under coordinate transformations. In addition to the time-sliced definition, the author gives a perturbative definition of path integrals which makes them invariant under coordinate transformations. A consistent implementation of this property leads to an extension of the theory of generalized functions by defining uniquely integrals over products of distributions. The powerful Feynman–Kleinert variational approach is explained and developed systematically into a variational perturbation theory which, in contrast to ordinary perturbation theory, produces convergent expansions. The convergence is uniform from weak to strong couplings, opening a way to precise approximate evaluations of analytically unsolvable path integrals. Tunneling processes are treated in detail. The results are used to determine the lifetime of supercurrents, the stability of metastable thermodynamic phases, and the large-order behavior of perturbation expansions. A new variational treatment extends the range of validity of previous tunneling theories from large to small barriers. A corresponding extension of large-order perturbation theory also applies now to small orders. Special attention is devoted to path integrals with topological restrictions. These are relevant to the understanding of the statistical properties of elementary particles and the entanglement phenomena in polymer physics and biophysics. The Chern–Simons theory of particles with fractional statistics (anyons) is introduced and applied to explain the fractional quantum Hall effect. The relevance of path integrals to financial markets is discussed, and improvements of the famous Black–Scholes formula for option prices are given which account for the fact that large market fluctuations occur much more frequently than in the commonly used Gaussian distributions. The author's other book on ‘Critical Properties of φ4 Theories’ gives a thorough introduction to the field of critical phenomena and develops new powerful resummation techniques for the extraction of physical results from the divergent perturbation expansions.
Download or read book Mathematical Reviews written by and published by . This book was released on 2008 with total page 984 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Strong Coupling Gauge Theories and Effective Field Theories written by Masayasu Harada and published by World Scientific. This book was released on 2003 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the important recent progress in both theoretical and phenomenological issues of strong coupling gauge theories, with/without supersymmetry and extra dimensions, etc. Emphasis is placed on dynamical symmetry breaking with large anomalous dimensions governed by the dynamics near the nontrivial fixed point. Also presented are recent developments of the corresponding effective field theories, such as those including light spectra other than the NambuOCoGoldstone particles. This book is a must for all those who are interested in dynamical symmetry breaking and effective field theories in a modern version. Contents: Light-Front Quantization of Gauge Theories (S J Brodsky); Significance of the Renormalization Constant of the Color Gauge Field (K Nishijima & M Chaichian); Mass Gap and Color Confinement in YangOCoMills Theory Based on Asymptotic Solutions of SD Equation (K-I Kondo); Strong Coupling Approach to Transverse Lattice QCD (S Dalley); Vector Manifestation of Chiral Symmetry (M Harada); Locking Internal and Space-Symmetries: Relativistic Vector Condensation (F Sannino); A Practical Gauge Invariant Construction of Abelian Chiral Gauge Theories on the Lattice (Y Kikukawa); Neutrino Masses in Theories with Dynamical Breaking of Electroweak and Extended Gauge Symmetries (T Appelquist & R Schrock); Dynamical Electroweak Symmetry Breaking from Extra Dimensions (M Hashimoto et al.); Classical Solutions of Field Equations in Randall Sundrum Brane Worlds (D Karasik et al.); Flavor Constraints on Theory Space (E H Simmons et al.); Neutrino Mass Matrix in Terms of Up-Quark Masses (M Bando & M Obara); and other papers. Readership: Graduate students and researchers in high energy physics, particularly those interested in dynamical symmetry breaking and effective field theories."
Download or read book Proceedings of the Second International Symposium on Quantum Theory and Symmetries written by Edward Kapuścik and published by World Scientific. This book was released on 2002 with total page 656 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the up-to-date status of quantum theory and the outlook for its development in the 21st century. The covered topics include basic problems of quantum physics, with emphasis on the foundations of quantum theory, quantum computing and control, quantum optics, coherent states and Wigner functions, as well as on methods of quantum physics based on Lie groups and algebras, quantum groups and noncommutative geometry.
