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Einstein's Special Relativity (E-SR) is the cornerstone of physics. De Sitter invariant SR (dS/AdS-SR) is a natural extension of E-SR, hence it relates to the foundation of physics. This book provides a description to dS/AdS-SR in terms of Lagrangian-Hamiltonian formulation associated with spacetime metric of inertial reference frames. One of the outstanding features of the book is as follows: All discussions on SR are in the inertial reference frames. This is a requirement due to the first principle of SR theory. The descriptions on dS/AdS-SR in this book satisfy this principle. For the curved spacetime in dS/AdS-SR theory, it is highly non-trivial. Contents:General IntroductionOverview of Einstein's Special Relativity (E-SR)De Sitter Invariant Special RelativityDe Sitter Invariant General RelativityDynamics of Expansion of the Universe in General RelativityRelativistic Quantum Mechanics for de Sitter Invariant Special RelativityDistant Hydrogen Atom in CosmologyTemporal and Spatial Variation of the Fine Structure ConstantDe Sitter Invariance of Generally Covariant Dirac Equation Readership: Students and professionals who are interested in de Sitter and anti-de Sitter invariant Special Relativity. Key Features:This is the first book to describe dS/AdS-SR systematically and comprehensivelyThe crucial contributions to dS/AdS-SR due to Lu–Zou–Guo's work (1970's) are interpreted in detail in this book. The conceptions of dS/AdS-SR Mechanics, dS/AdS-SR Quantum Mechanics, dS/AdS-SR General Relativity, and effects of dS/AdS-SR Cosmology are introduced in the book. In the descriptions, many techniques are involvedThe author, Professor Mu-Lin Yan, is an expert in SR, GR, Black Hole Physics, and Particle Physics. He is one of the discoverers of Nieh–Yan topological identity (1982), High genus solution of Yang–Baxter equation of chiral Potts model (1987), and some unusual hadron's states (2005). He also has contributions to the calculations of entropies of black holes, and to the studies of non-perturbative QCDKeywords:De Sitter Invariant Special Relativity;Special Relativity;De Sitter Group
This book presents the Projective approach to de Sitter Relativity. It traces the development of renewed interest in models of the universe at constant positive curvature such as "vacuum" geometry. The De Sitter Theory of Relativity, formulated in 1917 with Willem De Sitter's solution of the Einstein equations, was used in different fields during the 1950s and 1960s, in the work of H. Bacry, J.M. LevyLeblond and F.Gursey, to name some important contributors. From the 1960s to 1980s, L. Fantappié and G. Arcidiacono provided an elegant group approach to the De Sitter universe putting the basis for special and general projective relativity. Today such suggestions flow into a unitary scenario, and this way the De Sitter Relativity is no more a "missing opportunity" (F. Dyson, 1972), but has a central role in theoretical physics. In this volume a systematic presentation is given of the De Sitter Projective relativity, with the recent developments in projective general relativity and quantum cosmology.
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 43. Chapters: Graviton, Planck scale, Causal sets, De Sitter invariant special relativity, Event symmetry, Noncommutative geometry, AdS/CFT correspondence, Mathematical universe hypothesis, Invariance mechanics, Causal dynamical triangulation, Quantum mechanics of time travel, Gravitational instanton, Gravastar, Canonical quantum gravity, CGHS model, Gravitino, List of quantum gravity researchers, Membrane paradigm, Acoustic metric, Black hole electron, Wheeler-DeWitt equation, Dark energy star, Quantum foam, Chronon, Green-Schwarz mechanism, Quantum field theory in curved spacetime, Geon, Black hole complementarity, Black star, Rolling ball argument, BTZ black hole, Quantum geometry, Ho?ava-Lifshitz gravity, Bousso's holographic bound, Swampland, Gravitational anomaly, Virtual black hole, Causal patch, Abstract differential geometry, 2+1D topological gravity, Trans-Planckian problem, Group field theory, Mixed anomaly, Quantum cosmology, Pregeometry, Euclidean quantum gravity, Schr dinger-Newton equations, Composite gravity, Gauged supergravity, Weinberg-Witten theorem, IR/UV mixing, Nuts and bolts, Diffeomorphism constraint, Minisuperspace, Quantum gravity epoch, MTZ black hole. Excerpt: Quantum gravity (QG) is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics (describing 3 of the 4 known fundamental interactions) with general relativity (describing the fourth, gravity). It is hoped that development of such a theory would unify in a single consistent model all fundamental interactions and to describe all known observable interactions in the universe, at both microscopic and cosmic scale. Such theories would yield the same experimental results as ordinary quantum mechanics in conditions of weak gravity (potentials much less than c) and the same results as Einsteinian general...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 174. Chapters: Speed of light, Twin paradox, Lorentz transformation, Michelson-Morley experiment, List of relativistic equations, Mass-energy equivalence, History of special relativity, Lorentz ether theory, Introduction to special relativity, Lorentz group, Time dilation, Mass in special relativity, Gyrovector space, De Sitter invariant special relativity, Fourth dimension, Length contraction, Minkowski diagram, Covariant formulation of classical electromagnetism, Moving magnet and conductor problem, Velocity-addition formula, Variable speed of light, Relativistic heat conduction, Relativistic electromagnetism, Relativity of simultaneity, Cherenkov radiation, Minkowski space, Relativistic Doppler effect, Ladder paradox, Doubly-special relativity, Status of special relativity, Split-quaternion, Biquaternion, One-way speed of light, Lorentz covariance, Consequences of special relativity, Relativistic quantum chemistry, Klein-Gordon equation, Classical electromagnetism and special relativity, Emission theory, Olinto De Pretto, Observer, Inhomogeneous electromagnetic wave equation, Postulates of special relativity, Rapidity, Algebra of physical space, Thomas precession, Lorentz factor, Hafele-Keating experiment, Experiments of Rayleigh and Brace, Trouton-Rankine experiment, Superradiance, Sokolov-Ternov effect, Lorentz-Heaviside units, Test theories of special relativity, Ives-Stilwell experiment, Rietdijk-Putnam argument, Terrell rotation, Tachyonic antitelephone, Fock-Lorentz symmetry, Lorentz transformation under symmetric configuration, Static interpretation of time, Relativistic wave equations, Massless particle, Light-dragging effects, Kinetic momentum, Preferred frame, Kennedy-Thorndike experiment, Energy-momentum relation, Rest frame, Kith, Ultrarelativistic limit, Relativistic Euler equations, Relativistic aberration, Bondi...
The purposes of this book are (1) to explore and expound relativity physics and four-dimensional symmetry from the logically simplest viewpoint by making one single postulate instead of two; and (2) to indicate the simplest generalization of the Lorentz transformation in order to cope with frames with constant linear accelerations. The fundamentally new ideas of the first purpose are developed on the basis of the term paper of a Harvard physics undergraduate. They lead to an unexpected affirmative answer to the long-standing question of whether it is possible to construct a relativity theory without postulating the constancy of the speed of light and retaining only the first postulate of special relativity. This question was discussed in the early years following the discovery of special relativity by many physicists, including Ritz, Tolman, Kunz, Comstock and Pauli, all of whom obtained negative answers. Furthermore, the new theory of relativity indicates the truly universal and fundamental constants in physics, and provides a broad view of relativistic physics beyond special relativity. It substantiates the view and sheds light on the understanding that the four-dimensional symmetry framework can accommodate many different concepts of physical time, including common time and Reichenbach's general concept of time. This logically simplest viewpoint of relativity allows a natural extension of the physics of particles and fields from inertial frames to noninertial frames in which the speed of light is not constant. New predictions in physics resulting from this new viewpoint are discussed. The book is based on papers by the author and his collaborators in Physics Letters A, Nuovo Cimento B, and Physical Review A and D. Contents:A Brief Review of Space and TimeThe Nontrivial Pursuit of Earth's Absolute MotionOn the Right Track — Voigt, Lorentz and LarmorePoincaré's Contributions and the Aether (Past and Present)Young Einstein's Novel Creation Based on 2 PostulatesMinkowski's 4-Dimensional Spacetime, Adjustable Clocks and Flexibility in the Concept of TimeTaiji Relativity Based Solely on 1 Principle — the First Principle of RelativityThe Arbitrary Speed of Light in Taiji Relativity and the Michelson-Morley ExperimentLorentz and Poincaré Invariance Without Involving a Constant Corresponding to the Speed of LightTruly Universal Constants and Physical Laws Based on Taiji RelativityQuantum Electrodynamics Based on Taiji Relativity and Dilatation of Lifetimes and Decay-LengthsCommon Relativity: A Common Time for all ObserversCommon Time and Many-Particle Systems in a 4-Dimensional Symmetry FrameworkCommon Relativity and Quantum MechanicsCommon Relativity and Fuzzy Quantum Field TheoryCommon Relativity and the 3 K Cosmic Background RadiationExtended Relativity: A Weaker Postulate for the Speed of LightExtended Relativity with the Lorentz Group and Lifetime DilatationPhysical Implications of Extended RelativityDetermination of the Parameters of General Linear Transformations by Precision ExperimentsGeneralized Lorentz Transformations for Non-Inertial Frames Based on the Limiting 4-Dimensional SymmetryDynamics of Classical and Quantum Particles in Non-Inertial Frames with the Limiting 4-Dimensional SymmetryExperimental Tests of Generalized Lorentz Transformations for Constant-Linear-Acceleration FramesQuantizations of Scalar, Spinor and Electromagnetic Fields in Constant-Linear-Acceleration FramesTaiji Rotational Transformations with the Limiting 4-Dimensional Symmetry Readership: Theoretical, high-energy and experimental physicists. Keywords:Space;Time;Spacetime;Relativity;Lorentz;Poincare;Einstein;Minkowski;Symmetry;Invariance;Light;JP HsuReviews: “Hsu's book shows many new aspects of Einstein's theory which are not taught in lectures or by any other books on this subject … His understanding and appreciation of physics together with his unconventional style of writing make, in my opinion, the book worth reading for every physicist who is interested in Special Relativity.” Andreas Ernst University of Heidelberg Heidelberg, Germany
This book stresses the unifying power of the geometrical framework in bringing together concepts from the different areas of physics. Common underpinnings of optics, elasticity, gravitation, relativistic fields, particle mechanics and other subjects are underlined. It attempts to extricate the notion of space currently in the physical literature from the metric connotation. The book's goal is to present mathematical ideas associated with geometrical physics in a rather introductory language. Included are many examples from elementary physics and also, for those wishing to reach a higher level of understanding, a more advanced treatment of the mathematical topics. It is aimed as an elementary text, more so than most others on the market, and is intended for first year graduate students. Contents:ManifoldsDifferentiable StructureFinal TouchMathematical TopicsPhysical TopicsGlossaryReferencesAlphabetic Index Readership: Mathematical physicists. keywords:Manifolds;Differential Geometry;Differential Forms;Symmetries;Variational Calculus;Hamiltonian Mechanics;Elasticity;Relativistic Fields;Gauge Fields;General Relativity
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 151. Chapters: Nash embedding theorem, Conformal map, Curvature, Geodesic, Riemannian manifold, Riemann curvature tensor, Metric tensor, Holonomy, Symmetric space, De Sitter invariant special relativity, Covariance and contravariance of vectors, Geometrization conjecture, Systolic geometry, Covariant derivative, Hodge dual, Einstein notation, Ricci curvature, Ricci flow, Spin structure, Exponential map, List of formulas in Riemannian geometry, Introduction to systolic geometry, Christoffel symbols, Laplace-Beltrami operator, Glossary of Riemannian and metric geometry, Parallel transport, Gauss-Codazzi equations, Curvature of Riemannian manifolds, Gauss's lemma, Uniformization theorem, Levi-Civita connection, Ricci decomposition, Second fundamental form, Sectional curvature, De Sitter-Schwarzschild metric, Poincare metric, Calibrated geometry, Gravitational instanton, De Sitter space, Calculus of moving surfaces, Hermitian manifold, Tortuosity, Weyl tensor, Scalar curvature, Harmonic map, Cartan-Hadamard theorem, Pseudo-Riemannian manifold, Lie bracket of vector fields, Hermitian symmetric space, Spherical 3-manifold, Geodesics as Hamiltonian flows, Kahler manifold, Abel-Jacobi map, Jacobi field, Constraint counting, Clifford bundle, Killing vector field, Normal coordinates, Systoles of surfaces, Curved space, Fundamental theorem of Riemannian geometry, Theorema Egregium, Hyperkahler manifold, Unit tangent bundle, Sasakian manifold, Loewner's torus inequality, Cartan-Karlhede algorithm, Pu's inequality, Gauss map, Einstein manifold, Recurrent tensor, Soul theorem, Harmonic coordinates, Ruppeiner geometry, Filling radius, G2 manifold, Sub-Riemannian manifold, Quaternion-Kahler manifold, Frobenius manifold, Gromov-Hausdorff convergence, Cheng's eigenvalue comparison theorem, Gromov's systolic inequality for...

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