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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
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...
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.
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
These proceedings contain an up-to-date series of lectures covering issues at the forefront of cosmology, gravitation, and astrophysics. Both observational matters, such as accelerated expansion of the universe, and gamma ray bursts and theoretical issues, such as loop quantum gravity and quantum field theory in de Sitter space are presented. Being a school for advanced students, many of the lectures were a high level revision of recent developments, among which could single out the results presented by Belinski regarding the absence of black hole evaporation, and Riffini regarding the origin of gamma-0 ray bursts.
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...
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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