Download or read book The Theory of Sprays and Finsler Spaces with Applications in Physics and Biology written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book has been written by two mathematicians and one physicist: a pure mathematician specializing in Finsler geometry (Makoto Matsumoto), one working in mathematical biology (Peter Antonelli), and a mathematical physicist specializing in information thermodynamics (Roman Ingarden). The main purpose of this book is to present the principles and methods of sprays (path spaces) and Finsler spaces together with examples of applications to physical and life sciences. It is our aim to write an introductory book on Finsler geometry and its applications at a fairly advanced level. It is intended especially for graduate students in pure mathemat ics, science and applied mathematics, but should be also of interest to those pure "Finslerists" who would like to see their subject applied. After more than 70 years of relatively slow development Finsler geometry is now a modern subject with a large body of theorems and techniques and has math ematical content comparable to any field of modern differential geometry. The time has come to say this in full voice, against those who have thought Finsler geometry, because of its computational complexity, is only of marginal interest and with prac tically no interesting applications. Contrary to these outdated fossilized opinions, we believe "the world is Finslerian" in a true sense and we will try to show this in our application in thermodynamics, optics, ecology, evolution and developmental biology. On the other hand, while the complexity of the subject has not disappeared, the modern bundle theoretic approach has increased greatly its understandability.
Download or read book The Theory of Finslerian Laplacians and Applications written by P.L. Antonelli and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finslerian Laplacians have arisen from the demands of modelling the modern world. However, the roots of the Laplacian concept can be traced back to the sixteenth century. Its phylogeny and history are presented in the Prologue of this volume. The text proper begins with a brief introduction to stochastically derived Finslerian Laplacians, facilitated by applications in ecology, epidemiology and evolutionary biology. The mathematical ideas are then fully presented in section II, with generalizations to Lagrange geometry following in section III. With section IV, the focus abruptly shifts to the local mean-value approach to Finslerian Laplacians and a Hodge-de Rham theory is developed for the representation on real cohomology classes by harmonic forms on the base manifold. Similar results are proved in sections II and IV, each from different perspectives. Modern topics treated include nonlinear Laplacians, Bochner and Lichnerowicz vanishing theorems, Weitzenböck formulas, and Finslerian spinors and Dirac operators. The tools developed in this book will find uses in several areas of physics and engineering, but especially in the mechanics of inhomogeneous media, e.g. Cofferat continua. Audience: This text will be of use to workers in stochastic processes, differential geometry, nonlinear analysis, epidemiology, ecology and evolution, as well as physics of the solid state and continua.
Download or read book Differential Geometry of Spray and Finsler Spaces written by Zhongmin Shen and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we study sprays and Finsler metrics. Roughly speaking, a spray on a manifold consists of compatible systems of second-order ordinary differential equations. A Finsler metric on a manifold is a family of norms in tangent spaces, which vary smoothly with the base point. Every Finsler metric determines a spray by its systems of geodesic equations. Thus, Finsler spaces can be viewed as special spray spaces. On the other hand, every Finsler metric defines a distance function by the length of minimial curves. Thus Finsler spaces can be viewed as regular metric spaces. Riemannian spaces are special regular metric spaces. In 1854, B. Riemann introduced the Riemann curvature for Riemannian spaces in his ground-breaking Habilitationsvortrag. Thereafter the geometry of these special regular metric spaces is named after him. Riemann also mentioned general regular metric spaces, but he thought that there were nothing new in the general case. In fact, it is technically much more difficult to deal with general regular metric spaces. For more than half century, there had been no essential progress in this direction until P. Finsler did his pioneering work in 1918. Finsler studied the variational problems of curves and surfaces in general regular metric spaces. Some difficult problems were solved by him. Since then, such regular metric spaces are called Finsler spaces. Finsler, however, did not go any further to introduce curvatures for regular metric spaces. He switched his research direction to set theory shortly after his graduation.
Download or read book Finsler and Lagrange Geometries written by Mihai Anastasiei and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last decade several international conferences on Finsler, Lagrange and Hamilton geometries were organized in Bra§ov, Romania (1994), Seattle, USA (1995), Edmonton, Canada (1998), besides the Seminars that periodically are held in Japan and Romania. All these meetings produced important progress in the field and brought forth the appearance of some reference volumes. Along this line, a new International Conference on Finsler and Lagrange Geometry took place August 26-31,2001 at the "Al.I.Cuza" University in Ia§i, Romania. This Conference was organized in the framework of a Memorandum of Un derstanding (1994-2004) between the "Al.I.Cuza" University in Ia§i, Romania and the University of Alberta in Edmonton, Canada. It was especially dedicated to Prof. Dr. Peter Louis Antonelli, the liaison officer in the Memorandum, an untired promoter of Finsler, Lagrange and Hamilton geometries, very close to the Romanian School of Geometry led by Prof. Dr. Radu Miron. The dedica tion wished to mark also the 60th birthday of Prof. Dr. Peter Louis Antonelli. With this occasion a Diploma was given to Professor Dr. Peter Louis Antonelli conferring the title of Honorary Professor granted to him by the Senate of the oldest Romanian University (140 years), the "Al.I.Cuza" University, Ia§i, Roma nia. There were almost fifty participants from Egypt, Greece, Hungary, Japan, Romania, USA. There were scheduled 45 minutes lectures as well as short communications.
Download or read book Teaching the World written by Merrill Distad and published by University of Alberta. This book was released on 1996-04 with total page 52 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book catalogues an exhibition of textbooks by authors from the University of Alberta. Each finished textbook contains its own story of challenges and victories. And each has its own power as a record of knowledge, a teaching tool, and an object of permanence and beauty.
Download or read book Causality and Locality in Modern Physics written by G. Hunter and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Symposium entitled: Causality and Locality in Modern Physics and As tronomy: Open Questions and Possible Solutions was held at York University, Toronto, during the last week of August 1997. It was a sequel to a similar sym posium entitled: The Present Status of the Quantum Theory of Light held at the same venue in August 1995. These symposia came about as a result of discussions between Professor Stanley Jeffers and colleagues on the International Organizing Committee. Professor Jeffers was the executive local organizer of the symposia. The 1997 symposium attracted over 120 participants representing 26 different countries and academic institutions. The broad theme of both symposia was the enigma of modern physics: the non-local, and possibly superluminal interactions implied by quantum mechanics, the structure of fundamental particles including the photon, the reconciliation of quantum mechanics with the theory of relativity, and the nature of gravity and inertia. Jean-Pierre Vigier was the guest of honour at both symposia. He was a lively contributor to the discussions of the presentations. The presentations were made as 30-minute lectures, or during an evening poster session. Some participants did not submit a written account of their presentation at the symposium, and not all of the articles submitted for the Proceedings could be included because of the publisher's page limit. The titles and authors of the papers that had to be excluded are listed in an appendix.
Download or read book Topics in Contemporary Differential Geometry Complex Analysis and Mathematical Physics written by Stancho Dimiev and published by World Scientific. This book was released on 2007 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the contributions by the participants in the eight of a series workshops in complex analysis, differential geometry and mathematical physics and related areas.Active specialists in mathematical physics contribute to the volume, providing not only significant information for researchers in the area but also interesting mathematics for non-specialists and a broader audience. The contributions treat topics including differential geometry, partial differential equations, integrable systems and mathematical physics.
Download or read book Theory of the Electron written by J. Keller and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the first century after its discovery, the electron has come to be a fundamental element in the analysis of physical aspects of nature. This book is devoted to the construction of a deductive theory of the electron, starting from first principles and using a simple mathematical tool, geometric analysis. Its purpose is to present a comprehensive theory of the electron to the point where a connection can be made with the main approaches to the study of the electron in physics. The introduction describes the methodology. Chapter 2 presents the concept of space-time-action relativity theory and in chapter 3 the mathematical structures describing action are analyzed. Chapters 4, 5, and 6 deal with the theory of the electron in a series of aspects where the geometrical analysis is more relevant. Finally in chapter 7 the form of geometrical analysis used in the book is presented to elucidate the broad range of topics which are covered and the range of mathematical structures which are implicitly or explicitly included. The book is directed to two different audiences of graduate students and research scientists: primarily to theoretical physicists in the field of electron physics as well as those in the more general field of quantum mechanics, elementary particle physics, and general relativity; secondly, to mathematicians in the field of geometric analysis.
Download or read book Isodual Theory of Antimatter written by Ruggero Maria Santilli and published by Springer Science & Business Media. This book was released on 2006-02-28 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: The scope of this monograph is to show that our classical, quantum and cosmological knowledge of antimatter is at its beginning with much yet to be discovered, and that a commitment to antimatter by experimentalists will be invaluable to antimatter science. This is also the first book presenting the isodual theory of antimatter. It is aimed at scientists and researchers in theoretical physics.
Download or read book The Landscape of Theoretical Physics A Global View written by M. Pavsic and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Today many important directions of research are being pursued more or less independently of each other. These are, for instance, strings and mem branes, induced gravity, embedding of spacetime into a higher dimensional space, the brane world scenario, the quantum theory in curved spaces, Fock Schwinger proper time formalism, parametrized relativistic quantum the ory, quantum gravity, wormholes and the problem of “time machines”, spin and supersymmetry, geometric calculus based on Clifford algebra, various interpretations of quantum mechanics including the Everett interpretation, and the recent important approach known as “decoherence”. A big problem, as I see it, is that various people thoroughly investigate their narrow field without being aware of certain very close relations to other fields of research. What we need now is not only to see the trees but also the forest. In the present book I intend to do just that: to carry out a first approximation to a synthesis of the related fundamental theories of physics. I sincerely hope that such a book will be useful to physicists. From a certain viewpoint the book could be considered as a course in the oretical physics in which the foundations of all those relevant fundamental theories and concepts are attempted to be thoroughly reviewed. Unsolved problems and paradoxes are pointed out. I show that most of those ap proaches have a common basis in the theory of unconstrained membranes. The very interesting and important concept of membrane space, the tensor calculus in and functional transformations in are discussed.
Download or read book Reading Bohr Physics and Philosophy written by Arkady Plotnitsky and published by Springer Science & Business Media. This book was released on 2006-11-15 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a new perspective on Niels Bohr's interpretation of quantum mechanics as complementarity, and on the relationships between physics and philosophy in Bohr's work. The importance of quantum field theory for Bohr's thinking has not been adequately addressed in the literature on Bohr. This book provides clarification of Bohr's writings (which usually pose problems of reading), and an analysis of the role of quantum field theory in Bohr's thinking.
Download or read book A Sampler of Riemann Finsler Geometry written by David Dai-Wai Bao and published by Cambridge University Press. This book was released on 2004-11 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: These expository accounts treat issues related to volume, geodesics, curvature and mathematical biology, with instructive examples.
Download or read book Kinematical Theory of Spinning Particles written by M. Rivas and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical spin is described in terms of velocities and acceleration so that knowledge of advanced mathematics is not required. Written in the three-dimensional notation of vector calculus, it can be followed by undergraduate physics students, although some notions of Lagrangian dynamics and group theory are required. It is intended as a general course at a postgraduate level for all-purpose physicists. This book presents a unified approach to classical and quantum mechanics of spinning particles, with symmetry principles as the starting point. A classical concept of an elementary particle is presented. The variational statements to deal with spinning particles are revisited. It is shown that, by explicitly constructing different models, symmetry principles are sufficient for the description of either classical or quantum-mechanical elementary particles. Several spin effects are analyzed.
Download or read book Cosmological Pattern of Microphysics in the Inflationary Universe written by Maxim Y. Khlopov and published by Springer Science & Business Media. This book was released on 2013-03-20 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern cosmology is a quickly developing ?eld of research. New technical devices and tools supply the community with new experimental data measured with high accuracy. The self-consistent explanation of these data needs t- oretical models that are based on hypothetical predictions of particle theory. In their turn, such predictions imply cosmology for their probe. Speci?c st- ies of the cosmological consequences of particle theory, linking them to their observable signatures, are actual. This boiling kettle of theoretical research and experimental efforts produces ideas that will be preserved for following generations. The aim of this book is to acquaint the reader with some of these ideas, - fering nontrivial ways to probe the physical basis of modern cosmology. An extensive review of the newest ideas in modern cosmology, e. g. , related with the development of the M-brane theory, lies beyond the scope of our book, which is aimed at providing a ?rmly established system of probes for these ideas, linking their predictions to their possible experimental test. We use the framework of in?ationary paradigm to reveal the phenomena that can shed light on the physical origin of the observed Universe, of its matter content and large-scale structure. The crucial role of quantum ?uctuations in creation of our Universe and in possible features, re?ecting cosmological impact of microphysics, is discussed. These features are shown to be accessible to - perimental test in the near future.
Download or read book Theory of High Temperature Superconductivity written by S. Fujita and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Flux quantization experiments indicate that the carriers, Cooper pairs (pairons), in the supercurrent have charge magnitude 2e, and that they move independently. Josephson interference in a Superconducting Quantum Int- ference Device (SQUID) shows that the centers of masses (CM) of pairons move as bosons with a linear dispersion relation. Based on this evidence we develop a theory of superconductivity in conventional and mate- als from a unified point of view. Following Bardeen, Cooper and Schrieffer (BCS) we regard the phonon exchange attraction as the cause of superc- ductivity. For cuprate superconductors, however, we take account of both optical- and acoustic-phonon exchange. BCS started with a Hamiltonian containing “electron” and “hole” kinetic energies and a pairing interaction with the phonon variables eliminated. These “electrons” and “holes” were introduced formally in terms of a free-electron model, which we consider unsatisfactory. We define “electrons” and “holes” in terms of the cur- tures of the Fermi surface. “Electrons” (1) and “holes” (2) are different and so they are assigned with different effective masses: Blatt, Schafroth and Butler proposed to explain superconductivity in terms of a Bose-Einstein Condensation (BEC) of electron pairs, each having mass M and a size. The system of free massive bosons, having a quadratic dispersion relation: and moving in three dimensions (3D) undergoes a BEC transition at where is the pair density.
Download or read book Nonperturbative Quantum Field Theory and the Structure of Matter written by T. Borne and published by Springer Science & Business Media. This book was released on 2005-12-19 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book, which presents a new view of quantum field theory, may serve as a research monograph and an alternative textbook examining topics which are not usually treated in conventional works." "Audience: This volume will appeal to researchers concerned with the foundation of the theory of matter and forces including gravitation. It will also be interesting to those working with quantum field theoretic methods in various disciplines, such as particle physics, nuclear physics, condensed mater physics, and relativity."--Jacket.
Download or read book Classical Electromagnetic Theory written by Jack Vanderlinde and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: In questions of science, the authority of a thousand is not worth the humble reasoning of a single individual. Galileo Galilei, physicist and astronomer (1564-1642) This book is a second edition of “Classical Electromagnetic Theory” which derived from a set of lecture notes compiled over a number of years of teaching elect- magnetic theory to fourth year physics and electrical engineering students. These students had a previous exposure to electricity and magnetism, and the material from the ?rst four and a half chapters was presented as a review. I believe that the book makes a reasonable transition between the many excellent elementary books such as Gri?th’s Introduction to Electrodynamics and the obviously graduate level books such as Jackson’s Classical Electrodynamics or Landau and Lifshitz’ Elect- dynamics of Continuous Media. If the students have had a previous exposure to Electromagnetictheory, allthematerialcanbereasonablycoveredintwosemesters. Neophytes should probable spend a semester on the ?rst four or ?ve chapters as well as, depending on their mathematical background, the Appendices B to F. For a shorter or more elementary course, the material on spherical waves, waveguides, and waves in anisotropic media may be omitted without loss of continuity.
