Download or read book Energy And Geometry An Introduction To Deformed Special Relativity written by Fabio Cardone and published by World Scientific. This book was released on 2004-08-10 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses in detail the mathematical aspects and physical applications of a new geometrical structure of space-time. It is based on a generalization (”deformation”) of the usual Minkowski space, supposedly endowed with a metric whose coefficients depend on the energy.Energy and Geometry: Geometrical Description of Interactions is suitable for researchers, academics and students in mathematical and theoretical physics.This book has been selected for coverage in:• CC / Physical, Chemical & Earth Sciences• Index to Scientific Book Contents® (ISBC)
Download or read book Energy and Geometry written by Fabio Cardone and published by World Scientific. This book was released on 2004 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special Relativity (SR) is essentially grounded on the properties of space-time, i.e. isotropy of space and homogeneity of space and time (as a consequence of the equivalence of inertial frames) and on the Galilei principle of relativity.
Download or read book Energy Of Knots And Conformal Geometry written by Jun O'hara and published by World Scientific. This book was released on 2003-03-25 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy of knots is a theory that was introduced to create a “canonical configuration” of a knot — a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a “canonical configuration” of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments.
Download or read book Geometry and Physics of Branes written by U Bruzzo and published by CRC Press. This book was released on 2002-11-05 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: Branes are solitonic configurations of a string theory that are represented by extended objects in a higher-dimensional space-time. They are essential for a comprehension of the non-perturbative aspects of string theory, in particular, in connection with string dualities. From the mathematical viewpoint, branes are related to several important theo
Download or read book Geometry of the Fundamental Interactions written by M. D. Maia and published by Springer Science & Business Media. This book was released on 2011-06-14 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Yang-Mills theory of gauge interactions is a prime example of interdisciplinary mathematics and advanced physics. Its historical development is a fascinating window into the ongoing struggle of mankind to understand nature. The discovery of gauge fields and their properties is the most formidable landmark of modern physics. The expression of the gauge field strength as the curvature associated to a given connection, places quantum field theory in the same geometrical footing as the gravitational field of general relativity which is naturally written in geometrical terms. The understanding of such geometrical property may help one day to write a unified field theory starting from symmetry principles. Of course, there are remarkable differences between the standard gauge fields and the gravitational field, which must be understood by mathematicians and physicists before attempting such unification. In particular, it is important to understand why gravitation is not a standard gauge field. This book presents an account of the geometrical properties of gauge field theory, while trying to keep the equilibrium between mathematics and physics. At the end we will introduce a similar approach to the gravitational field.
Download or read book Quantum geometry written by Tell Andersson and published by . This book was released on 1984 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Geometry of Energy written by Ethan Indigo Smith and published by Createspace Independent Pub. This book was released on 2015-02-16 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ethan Indigo Smith explores a most empowering and effective form of meditation toward individuation. The Geometry of Energy is a simple and profound instruction on how to meditate using the simplest and most all encompassing aspects of geometry. It is a simple four step process to enhance and help begin your meditation practice. It is a wonderful meditation along with an impeccable understanding of energy and results in a transformation toward individuation, becoming your true nature.
Download or read book Geometry and Physics written by Jürgen Jost and published by Springer Science & Business Media. This book was released on 2009-08-17 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
Download or read book Power Geometry in Algebraic and Differential Equations written by A.D. Bruno and published by Elsevier. This book was released on 2000-08-03 with total page 397 pages. Available in PDF, EPUB and Kindle. Book excerpt: The geometry of power exponents includes the Newton polyhedron, normal cones of its faces, power and logarithmic transformations. On the basis of the geometry universal algorithms for simplifications of systems of nonlinear equations (algebraic, ordinary differential and partial differential) were developed. The algorithms form a new calculus which allows to make local and asymptotical analysis of solutions to those systems. The efficiency of the calculus is demonstrated with regard to several complicated problems from Robotics, Celestial Mechanics, Hydrodynamics and Thermodynamics. The calculus also gives classical results obtained earlier intuitively and is an alternative to Algebraic Geometry, Differential Algebra, Lie group Analysis and Nonstandard Analysis.
Download or read book Energy Has Shape written by Tell Andersson and published by . This book was released on 1985 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Little Book of Sacred Geometry written by Astrid Carvel and published by Summersdale. This book was released on 2023-02-09 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This accessible introduction to sacred geometry illuminates the beauty and power of nature and explains how we can draw on this mystical energy to enrich our everyday lives Sacred geometry is founded on the belief that everything is connected through the shapes and symmetries that we see repeated in nature all around us, from snowflakes and shells to crystals and honeycombs. These beautiful patterns are part of the mystic architecture of the universe - some even see them as the signature of a deity woven throughout creation. This beginner's guide clearly explains what sacred geometry is and how it manifests in the natural world. Then, by learning how to harness the power of sacred shapes, you can find healing, energy, peace and oneness with the universe. The Little Book of Sacred Geometry will help you appreciate the cosmic significance of these principles and grasp fascinating insights such as: How the study of sacred geometry has developed since ancient times What the numerous sacred shapes look like What key concepts, such as the golden ratio, refer to How sacred geometrical practices can be applied in your life
Download or read book Blow up Theory for Elliptic PDEs in Riemannian Geometry written by Olivier Druet and published by Princeton University Press. This book was released on 2009-01-10 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic equations of critical Sobolev growth have been the target of investigation for decades because they have proved to be of great importance in analysis, geometry, and physics. The equations studied here are of the well-known Yamabe type. They involve Schrödinger operators on the left hand side and a critical nonlinearity on the right hand side. A significant development in the study of such equations occurred in the 1980s. It was discovered that the sequence splits into a solution of the limit equation--a finite sum of bubbles--and a rest that converges strongly to zero in the Sobolev space consisting of square integrable functions whose gradient is also square integrable. This splitting is known as the integral theory for blow-up. In this book, the authors develop the pointwise theory for blow-up. They introduce new ideas and methods that lead to sharp pointwise estimates. These estimates have important applications when dealing with sharp constant problems (a case where the energy is minimal) and compactness results (a case where the energy is arbitrarily large). The authors carefully and thoroughly describe pointwise behavior when the energy is arbitrary. Intended to be as self-contained as possible, this accessible book will interest graduate students and researchers in a range of mathematical fields.
Download or read book The Sacred Geometry Guidebook written by Sergio Rijo and published by SERGIO RIJO. This book was released on 2023-08-07 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Sacred Geometry Guidebook: Illuminating the Power of Patterns" takes readers on an enlightening journey through the mysterious realm of sacred geometry. Delving into the divine secrets of ancient patterns, this comprehensive guidebook explores the deep spiritual connections and hidden knowledge carried by sacred shapes. From the timeless wisdom encoded within the Flower of Life to the magical properties of the golden ratio, readers will uncover the profound symbolism and significance of these geometric wonders. Throughout the book, readers will discover the omnipresence of sacred geometry in various cultural expressions, architecture, art, and the natural world. From ancient structures that possessed sacred shapes to the hidden geometry behind every number, this guidebook reveals how sacred geometry permeates every facet of human existence. Beyond mere theoretical exploration, "The Sacred Geometry Guidebook" empowers readers with practical applications. Understanding the science behind sacred geometry and its influence on the natural world, readers will learn how to harness the transformative power of these patterns for personal growth and spiritual evolution. By embracing sacred shapes in meditation, daily practices, and creative expressions, individuals can foster a deeper sense of unity and harmony with the universe. With its profound insights and easy-to-follow explanations, this guidebook is suitable for both beginners and enthusiasts of sacred geometry. Whether seeking spiritual enlightenment or simply curious about the mysteries of the universe, "The Sacred Geometry Guidebook: Illuminating the Power of Patterns" offers a captivating and transformative exploration into the magic and wisdom of sacred geometry.
Download or read book Physical Geometry written by Gustavo R Gonz Lez-Mart N and published by CreateSpace. This book was released on 2011-09-24 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is generally recognized that there exist problems in Physics. In particular, A. Einstein remained critical of some theoretical ideas in modern physics until his death. He was unsatisfied with his own gravitation and advocated the need for a fundamental unified theory which would include relativity, electromagnetism and gravitation from the beginning. He stated that the concepts of parallelism and differentiation are important. Furthermore, present models for Particle Physics are expressed in terms of a very large number of empirical parameters and a high number of dimensions. They are not clearly related to a fundamental underlying physical interaction. Gravitation and Electrodynamics are faced with serious theoretical challenges, particularly in Cosmic Physics due to the possible existence of dark matter and energy. Differential geometry offers the appropriate mathematical structure to accomplish Einstein's physical ideas. The key is "how to differentiate." In the book we use an Ehresmann connection, a concept related to groups. The group is determined from electrodynamics and relativity as the automorphisms of the space-time geometric algebra. Matter and fields are represented by generator-valued tensors. Unification is given by the fundamental nonlinear equation associated to the group. Microscopic physics is the study of linear excitations, which are group representations characterized by discrete numbers. Results obtained indicate that gravitation and electromagnetism are unified in a nontrivial manner. Odd generators represent non classical interactions. The equation of motion determines a geodesic motion with the Lorentz force term. The Einstein field equation with a purely geometric energy momentum tensor is obtained. In the newtonian limit, the constant geometric energy density of a hyperbolic symmetric solution is related to the gravitational constant G. Far from the limit the parameter G would be variable. This effect may be interpreted as dark matter. In vacuum, the known gravitational solutions are obtained. Electromagnetism is related to an SU(2) subgroup. If we restrict to the even U(1) subgroup we obtain Maxwell's equations. The equation of motion is a geometric generalization of Dirac's equation. This geometry is the germ of quantum physics including its probabilistic aspects. The geometric nature of Planck's constant h and of light speed c is determined by their relations to the connection and the metric. The alpha coupling constant is also determined geometrically. Mass is defined in terms of energy. The geometry shows various physical triple structures. The geometric excitations have quanta of charge, flux and spin which determine the fractional quantum Hall effect. The bare-mass quotients of the three stable particles are calculated giving a geometric expression for the proton-electron mass ratio, previously known but physically unexplained. There are connection excitations whose masses correspond to the weak boson masses and allow a geometric interpretation of Weinberg's angle. The equation of motion determines the anomalous bare magnetic moments of the proton, the electron and the neutron. The "strong" electromagnetic odd SU(2) part, generates short range attractive magnetic potentials which are sufficiently strong to determine the binding energy of the deuteron and other light nuclides. The bare masses of the leptons in the three families are calculated as topological excitations of the electron. The masses of these excitations increase under the action of a strong connection and are related to meson and quark masses. The mass spectrum for low masses agrees with the physical particle mass spectrum. The proton shows a triple structure that may be related to a quark structure. The combinations of the three fundamental geometric excitations (proton, electron and neutrino) form other excitations and may be used to represent particles showing a symmetry under the group SU(3)xSU(2)XU(1).
Download or read book Energy of Knots and Conformal Geometry written by Jun O'Hara and published by World Scientific. This book was released on 2003 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy of knots is a theory that was introduced to create a OC canonical configurationOCO of a knot OCo a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a OC canonical configurationOCO of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments. Contents: In Search of the OC Optimal EmbeddingOCO of a Knot: -Energy Functional E (); On E (2); L p Norm Energy with Higher Index; Numerical Experiments; Stereo Pictures of E (2) Minimizers; Energy of Knots in a Riemannian Manifold; Physical Knot Energies; Energy of Knots from a Conformal Geometric Viewpoint: Preparation from Conformal Geometry; The Space of Non-Trivial Spheres of a Knot; The Infinitesimal Cross Ratio; The Conformal Sin Energy E sin (c) Measure of Non-Trivial Spheres; Appendices: Generalization of the Gauss Formula for the Linking Number; The 3-Tuple Map to the Set of Circles in S 3; Conformal Moduli of a Solid Torus; Kirchhoff Elastica; Open Problems and Dreams. Readership: Graduate students and researchers in geometry & topology and numerical & computational mathematics."
Download or read book Theorems on Regularity and Singularity of Energy Minimizing Maps written by Leon Simon and published by Springer Science & Business Media. This book was released on 1996-03-28 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of these lecture notes is to give an essentially self-contained introduction to the basic regularity theory for energy minimizing maps, including recent developments concerning the structure of the singular set and asymptotics on approach to the singular set. Specialized knowledge in partial differential equations or the geometric calculus of variations is not required; a good general background in mathematical analysis would be adequate preparation.
Download or read book New Perspective On Relativity A An Odyssey In Non euclidean Geometries written by Bernard H Lavenda and published by World Scientific. This book was released on 2011-10-10 with total page 695 pages. Available in PDF, EPUB and Kindle. Book excerpt: Starting off from noneuclidean geometries, apart from the method of Einstein's equations, this book derives and describes the phenomena of gravitation and diffraction. A historical account is presented, exposing the missing link in Einstein's construction of the theory of general relativity: the uniformly rotating disc, together with his failure to realize, that the Beltrami metric of hyperbolic geometry with constant curvature describes exactly the uniform acceleration observed.This book also explores these questions:
