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Título : Einstein and the Changing Worldviews of Physics Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Lehner, Christoph ; Renn, Jürgen ; Schemmel, Matthias Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2012 Colección: Einstein Studies num. 12 Número de páginas: XII, 363 p. 21 illus., 5 illus. in color Il.: online resource ISBN/ISSN/DL: 978-0-8176-4940-1 Idioma : Inglés (eng) Palabras clave: Mathematics History Mathematical physics Gravitation Astronomy Astrophysics Cosmology Physics of Sciences Classical and Quantum Gravitation, Relativity Theory Astronomy, Philosophical Foundations Clasificación: 51 Matemáticas Resumen: This volume reviews conceptual conflicts at the foundations of physics now and in the past century. The focus is on the conditions and consequences of Einstein’s pathbreaking achievements that sealed the decline of the classical notions of space, time, radiation, and matter, and resulted in the theory of relativity. Particular attention is paid to the implications of conceptual conflicts for scientific views of the world at large, thus providing the basis for a comparison of the demise of the mechanical worldview at the turn of the 20th century with the challenges presented by cosmology at the turn of the 21st century. Throughout the work, Einstein’s contributions are not seen in isolation but instead set into the wider intellectual context of dealing with the problem of gravitation in the twilight of classical physics; the investigation of the historical development is carried out with a number of epistemological questions in mind, concerning, in particular, the transformation process of knowledge associated with the changing worldviews of physics. Einstein and the Changing Worldviews of Physics is divided into four main parts: * Part I: At the Limits of the Classical Worldview; * Part II: Contexts of the Relativity Revolution; * Part III: The Emergence of the Relativistic Worldview; * Part IV: A New Worldview in the Making. The contributions explore various aspects of the emerging relativistic views in modern physics by giving an historical, philosophical, and mathematical account of Einstein’s work, as well as the work of other distinguished physicists in the field. Taken as a whole, the book is focused on the interplay between mathematical concepts and physical ideas throughout history by studying today’s scientific world and how it continues to redefine physics in the 21st century. Contributors: A. Ashtekar, E. Battaner, J.E. Beckman, K.A. Brading, T. Dray, J. Eisenstaedt, E. Florido, H.F. Goenner, D. Kennefick, J. Renn, T.A. Ryckman, D.C. Salisbury, J.M. Sánchez-Ron, M. Schemmel, R. Schulmann, B.F. Schutz, J.M.M. Senovilla, A.T. Tolmasquim, R.M. Wald, G. Wolters Nota de contenido: Introduction -- Part I: At the Limits of the Classical Worldview -- Theories of Gravitation in the Twilight of Classical Physics -- The Newtonian Theory of Light Propagation -- Mach and Einstein, or, Clearing Troubled Waters in the History of Science -- Part II: Contexts of the Relativity Revolution -- Tilling the Seedbed of Einstein's Politics: A Pre-1905 Harbinger? -- The Early Reception of Einstein’s Relativity among British Philosophers -- Science and Ideology in Einstein's Visit to South America in 1925 -- The Reception of Einstein's Relativity Theories in Literature and the Arts (1920–1950) -- Part III: The Emergence of the Relativistic Worldview -- Hilbert’s Axiomatic Method and his "Foundations of Physics": Reconciling Causality with the Axiom of General Invariance -- Not Only Because of Theory: Dyson, Eddington and the Competing Myths of the 1919 Eclipse Expedition -- Peter Havas (1916–2004) -- Peter Bergmann and the Invention of Constrained Hamiltonian Dynamics -- Thoughts About a Conceptual Framework for Relativistic Gravity -- Part IV: A New Worldview in the Making -- Observational Tests of General Relativity: An Historical Look at Measurements Prior to the Advent of Modern Space-Borne Instruments -- Primordial Magnetic Fields and Cosmic Microwave Background -- Singularity Theorems in General Relativity: Achievements and Open Questions -- The History and Present Status of Quantum Field Theory in Curved Spacetime -- The Border Between Relativity and Quantum Theory -- The Issue of the Beginning in Quantum Gravity En línea: http://dx.doi.org/10.1007/978-0-8176-4940-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32671 Einstein and the Changing Worldviews of Physics [documento electrónico] / SpringerLink (Online service) ; Lehner, Christoph ; Renn, Jürgen ; Schemmel, Matthias . - Boston : Birkhäuser Boston, 2012 . - XII, 363 p. 21 illus., 5 illus. in color : online resource. - (Einstein Studies; 12) .
ISBN : 978-0-8176-4940-1
Idioma : Inglés (eng)
Palabras clave: Mathematics History Mathematical physics Gravitation Astronomy Astrophysics Cosmology Physics of Sciences Classical and Quantum Gravitation, Relativity Theory Astronomy, Philosophical Foundations Clasificación: 51 Matemáticas Resumen: This volume reviews conceptual conflicts at the foundations of physics now and in the past century. The focus is on the conditions and consequences of Einstein’s pathbreaking achievements that sealed the decline of the classical notions of space, time, radiation, and matter, and resulted in the theory of relativity. Particular attention is paid to the implications of conceptual conflicts for scientific views of the world at large, thus providing the basis for a comparison of the demise of the mechanical worldview at the turn of the 20th century with the challenges presented by cosmology at the turn of the 21st century. Throughout the work, Einstein’s contributions are not seen in isolation but instead set into the wider intellectual context of dealing with the problem of gravitation in the twilight of classical physics; the investigation of the historical development is carried out with a number of epistemological questions in mind, concerning, in particular, the transformation process of knowledge associated with the changing worldviews of physics. Einstein and the Changing Worldviews of Physics is divided into four main parts: * Part I: At the Limits of the Classical Worldview; * Part II: Contexts of the Relativity Revolution; * Part III: The Emergence of the Relativistic Worldview; * Part IV: A New Worldview in the Making. The contributions explore various aspects of the emerging relativistic views in modern physics by giving an historical, philosophical, and mathematical account of Einstein’s work, as well as the work of other distinguished physicists in the field. Taken as a whole, the book is focused on the interplay between mathematical concepts and physical ideas throughout history by studying today’s scientific world and how it continues to redefine physics in the 21st century. Contributors: A. Ashtekar, E. Battaner, J.E. Beckman, K.A. Brading, T. Dray, J. Eisenstaedt, E. Florido, H.F. Goenner, D. Kennefick, J. Renn, T.A. Ryckman, D.C. Salisbury, J.M. Sánchez-Ron, M. Schemmel, R. Schulmann, B.F. Schutz, J.M.M. Senovilla, A.T. Tolmasquim, R.M. Wald, G. Wolters Nota de contenido: Introduction -- Part I: At the Limits of the Classical Worldview -- Theories of Gravitation in the Twilight of Classical Physics -- The Newtonian Theory of Light Propagation -- Mach and Einstein, or, Clearing Troubled Waters in the History of Science -- Part II: Contexts of the Relativity Revolution -- Tilling the Seedbed of Einstein's Politics: A Pre-1905 Harbinger? -- The Early Reception of Einstein’s Relativity among British Philosophers -- Science and Ideology in Einstein's Visit to South America in 1925 -- The Reception of Einstein's Relativity Theories in Literature and the Arts (1920–1950) -- Part III: The Emergence of the Relativistic Worldview -- Hilbert’s Axiomatic Method and his "Foundations of Physics": Reconciling Causality with the Axiom of General Invariance -- Not Only Because of Theory: Dyson, Eddington and the Competing Myths of the 1919 Eclipse Expedition -- Peter Havas (1916–2004) -- Peter Bergmann and the Invention of Constrained Hamiltonian Dynamics -- Thoughts About a Conceptual Framework for Relativistic Gravity -- Part IV: A New Worldview in the Making -- Observational Tests of General Relativity: An Historical Look at Measurements Prior to the Advent of Modern Space-Borne Instruments -- Primordial Magnetic Fields and Cosmic Microwave Background -- Singularity Theorems in General Relativity: Achievements and Open Questions -- The History and Present Status of Quantum Field Theory in Curved Spacetime -- The Border Between Relativity and Quantum Theory -- The Issue of the Beginning in Quantum Gravity En línea: http://dx.doi.org/10.1007/978-0-8176-4940-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32671 Ejemplares
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Título : General Relativity Tipo de documento: documento electrónico Autores: Woodhouse, N. M. J ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2007 Colección: Springer Undergraduate Mathematics Series, ISSN 1615-2085 Número de páginas: X, 220 p. 33 illus Il.: online resource ISBN/ISSN/DL: 978-1-84628-487-8 Idioma : Inglés (eng) Palabras clave: Physics Applied mathematics Engineering Differential geometry Gravitation Astronomy Astrophysics Cosmology Classical and Quantum Gravitation, Relativity Theory Applications of Mathematics Theoretical, Mathematical Computational Geometry Astronomy, Clasificación: 51 Matemáticas Resumen: Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity. Although the original audience was made up of mathematics students, the focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle. At centre stage are the "local inertial coordinates" set up by an observer in free fall, in which special relativity is valid over short times and distances. In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors. The basic theory is presented using techniques, such as phase-plane analysis, that will already be familiar to mathematics undergraduates, and numerous problems, of varying levels of difficulty, are provided to test understanding. The latter chapters include the theoretical background to contemporary observational tests - in particular the detection of gravitational waves and the verification of the Lens-Thirring precession - and some introductory cosmology, to tempt the reader to further study. While primarily designed as an introduction for final-year undergraduates and first-year postgraduates in mathematics, the book is also accessible to physicists who would like to see a more mathematical approach to the ideas Nota de contenido: Newtonian Gravity -- Inertial Coordinates and Tensors -- Energy-Momentum Tensors -- Curved Space—Time -- Tensor Calculus -- Einstein’s Equation -- Spherical Symmetry -- Orbits in the Schwarzschild Space—Time -- Black Holes -- Rotating Bodies -- Gravitational Waves -- Redshift and Horizons En línea: http://dx.doi.org/10.1007/978-1-84628-487-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34583 General Relativity [documento electrónico] / Woodhouse, N. M. J ; SpringerLink (Online service) . - London : Springer London, 2007 . - X, 220 p. 33 illus : online resource. - (Springer Undergraduate Mathematics Series, ISSN 1615-2085) .
ISBN : 978-1-84628-487-8
Idioma : Inglés (eng)
Palabras clave: Physics Applied mathematics Engineering Differential geometry Gravitation Astronomy Astrophysics Cosmology Classical and Quantum Gravitation, Relativity Theory Applications of Mathematics Theoretical, Mathematical Computational Geometry Astronomy, Clasificación: 51 Matemáticas Resumen: Based on a course given at Oxford over many years, this book is a short and concise exposition of the central ideas of general relativity. Although the original audience was made up of mathematics students, the focus is on the chain of reasoning that leads to the relativistic theory from the analysis of distance and time measurements in the presence of gravity, rather than on the underlying mathematical structure. The geometric ideas - which are central to the understanding of the nature of gravity - are introduced in parallel with the development of the theory, the emphasis being on laying bare how one is led to pseudo-Riemannian geometry through a natural process of reconciliation of special relativity with the equivalence principle. At centre stage are the "local inertial coordinates" set up by an observer in free fall, in which special relativity is valid over short times and distances. In more practical terms, the book is a sequel to the author's Special Relativity in the same series, with some overlap in the treatment of tensors. The basic theory is presented using techniques, such as phase-plane analysis, that will already be familiar to mathematics undergraduates, and numerous problems, of varying levels of difficulty, are provided to test understanding. The latter chapters include the theoretical background to contemporary observational tests - in particular the detection of gravitational waves and the verification of the Lens-Thirring precession - and some introductory cosmology, to tempt the reader to further study. While primarily designed as an introduction for final-year undergraduates and first-year postgraduates in mathematics, the book is also accessible to physicists who would like to see a more mathematical approach to the ideas Nota de contenido: Newtonian Gravity -- Inertial Coordinates and Tensors -- Energy-Momentum Tensors -- Curved Space—Time -- Tensor Calculus -- Einstein’s Equation -- Spherical Symmetry -- Orbits in the Schwarzschild Space—Time -- Black Holes -- Rotating Bodies -- Gravitational Waves -- Redshift and Horizons En línea: http://dx.doi.org/10.1007/978-1-84628-487-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34583 Ejemplares
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Título : Lezioni di Relatività Generale e Teoria della Gravitazione : Per la Laurea Magistrale in Fisica Tipo de documento: documento electrónico Autores: Gasperini, Maurizio ; SpringerLink (Online service) Editorial: Milano : Springer Milan Fecha de publicación: 2010 Otro editor: Imprint: Springer Colección: UNITEXT, ISSN 2038-5714 Número de páginas: XVIII, 294 pagg Il.: online resource ISBN/ISSN/DL: 978-88-470-1421-3 Idioma : Italiano (ita) Palabras clave: Physics Gravitation Mechanics Astrophysics Elementary particles (Physics) Quantum field theory Classical and Gravitation, Relativity Theory Particles, Field Astroparticles Physics, general Clasificación: 51 Matemáticas Resumen: Un testo moderno e autosufficiente, specificatamente progettato per i corsi semestrali della Laurea Magistrale in Fisica, e accessibile a studenti di indirizzi diversi. Si parte dalle nozioni di base della Relatività Generale e si sviluppa la teoria gravitazionale classica fino a discutere temi di forte interesse attuale, come la fenomenologia delle onde gravitazionali, l’interazione gravitazionale dei campi spinoriali e l’estensione supersimmetrica delle equazioni di Einstein. Contiene le principali informazioni sulla teoria della gravitazione che al giorno d’oggi ogni laureato in Fisica dovrebbe possedere Nota de contenido: Complementi di relatività ristretta -- Verso una teoria relativistica della gravitazione -- Calcolo tensoriale in una varietà di Riemann -- Equazioni di Maxwell e geometria di Riemann -- Corpi di prova e segnali nello spazio-tempo di Riemann -- Deviazione geodetica e tensore di curvatura -- Equazioni di Einstein per il campo gravitazionale -- Approssimazione di campo debole -- Le onde gravitazionali -- La soluzione di Schwarzschild -- La soluzione di Kasner -- Tetradi e connessione di Lorentz -- Equazione di Dirac in un campo gravitazionale -- Supersimmetria e supergravità En línea: http://dx.doi.org/10.1007/978-88-470-1421-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33796 Lezioni di Relatività Generale e Teoria della Gravitazione : Per la Laurea Magistrale in Fisica [documento electrónico] / Gasperini, Maurizio ; SpringerLink (Online service) . - Milano : Springer Milan : Imprint: Springer, 2010 . - XVIII, 294 pagg : online resource. - (UNITEXT, ISSN 2038-5714) .
ISBN : 978-88-470-1421-3
Idioma : Italiano (ita)
Palabras clave: Physics Gravitation Mechanics Astrophysics Elementary particles (Physics) Quantum field theory Classical and Gravitation, Relativity Theory Particles, Field Astroparticles Physics, general Clasificación: 51 Matemáticas Resumen: Un testo moderno e autosufficiente, specificatamente progettato per i corsi semestrali della Laurea Magistrale in Fisica, e accessibile a studenti di indirizzi diversi. Si parte dalle nozioni di base della Relatività Generale e si sviluppa la teoria gravitazionale classica fino a discutere temi di forte interesse attuale, come la fenomenologia delle onde gravitazionali, l’interazione gravitazionale dei campi spinoriali e l’estensione supersimmetrica delle equazioni di Einstein. Contiene le principali informazioni sulla teoria della gravitazione che al giorno d’oggi ogni laureato in Fisica dovrebbe possedere Nota de contenido: Complementi di relatività ristretta -- Verso una teoria relativistica della gravitazione -- Calcolo tensoriale in una varietà di Riemann -- Equazioni di Maxwell e geometria di Riemann -- Corpi di prova e segnali nello spazio-tempo di Riemann -- Deviazione geodetica e tensore di curvatura -- Equazioni di Einstein per il campo gravitazionale -- Approssimazione di campo debole -- Le onde gravitazionali -- La soluzione di Schwarzschild -- La soluzione di Kasner -- Tetradi e connessione di Lorentz -- Equazione di Dirac in un campo gravitazionale -- Supersimmetria e supergravità En línea: http://dx.doi.org/10.1007/978-88-470-1421-3 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33796 Ejemplares
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Título : Non-Euclidean Geometries : János Bolyai Memorial Volume Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Prékopa, András ; Molnár, Emil Editorial: Boston, MA : Springer US Fecha de publicación: 2006 Colección: Mathematics and Its Applications num. 581 Número de páginas: XIII, 506 p Il.: online resource ISBN/ISSN/DL: 978-0-387-29555-8 Idioma : Inglés (eng) Palabras clave: Mathematics Geometry Differential geometry History Manifolds (Mathematics) Complex manifolds Gravitation of Mathematical Sciences and Cell Complexes (incl. Diff.Topology) Classical Quantum Gravitation, Relativity Theory Clasificación: 51 Matemáticas Resumen: "From nothing I have created a new different world,” wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics. Audience This book is intended for those who teach, study, and do research in geometry and history of mathematics. Cultural historians, physicists, and computer scientists will also find it an important source of information Nota de contenido: History -- The Revolution of János Bolyai -- Gauss and Non-Euclidean Geometry -- János Bolyai’s New Face -- Axiomatical and Logical Aspects -- Hyperbolic Geometry, Dimension-Free -- An Absolute Property of Four Mutually Tangent Circles -- Remembering Donald Coxeter -- Axiomatizations of Hyperbolic and Absolute Geometries -- Logical Axiomatizations of Space-Time. Samples from the Literature -- Polyhedra, Volumes, Discrete Arrangements, Fractals -- Structures in Hyperbolic Space -- The Symmetry of Optimally Dense Packings -- Flexible Octahedra in the Hyperbolic Space -- Fractal Geometry on Hyperbolic Manifolds -- A Volume Formula for Generalised Hyperbolic Tetrahedra -- Tilings, Orbifolds and Manifolds, Visualization -- The Geometry of Hyperbolic Manifolds of Dimension at Least 4 -- Real-Time Animation in Hyperbolic, Spherical, and Product Geometries -- On Spontaneous Surgery on Knots and Links -- Classification of Tile-Transitive 3-Simplex Tilings and Their Realizations in Homogeneous Spaces -- Differential Geometry -- Non-Euclidean Analysis -- Holonomy, Geometry and Topology of Manifolds with Grassmann Structure -- Hypersurfaces of Type Number 2 in the Hyperbolic Four-Space and Their Extensions To Riemannian Geometry -- How Far Does Hyperbolic Geometry Generalize? -- Geometry of the Point Finsler Spaces -- Physics -- Black Hole Perturbations -- Placing the Hyperbolic Geometry of Bolyai and Lobachevsky Centrally in Special Relativity Theory: An Idea Whose Time has Returned En línea: http://dx.doi.org/10.1007/0-387-29555-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34762 Non-Euclidean Geometries : János Bolyai Memorial Volume [documento electrónico] / SpringerLink (Online service) ; Prékopa, András ; Molnár, Emil . - Boston, MA : Springer US, 2006 . - XIII, 506 p : online resource. - (Mathematics and Its Applications; 581) .
ISBN : 978-0-387-29555-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Geometry Differential geometry History Manifolds (Mathematics) Complex manifolds Gravitation of Mathematical Sciences and Cell Complexes (incl. Diff.Topology) Classical Quantum Gravitation, Relativity Theory Clasificación: 51 Matemáticas Resumen: "From nothing I have created a new different world,” wrote János Bolyai to his father, Wolgang Bolyai, on November 3, 1823, to let him know his discovery of non-Euclidean geometry, as we call it today. The results of Bolyai and the co-discoverer, the Russian Lobachevskii, changed the course of mathematics, opened the way for modern physical theories of the twentieth century, and had an impact on the history of human culture. The papers in this volume, which commemorates the 200th anniversary of the birth of János Bolyai, were written by leading scientists of non-Euclidean geometry, its history, and its applications. Some of the papers present new discoveries about the life and works of János Bolyai and the history of non-Euclidean geometry, others deal with geometrical axiomatics; polyhedra; fractals; hyperbolic, Riemannian and discrete geometry; tilings; visualization; and applications in physics. Audience This book is intended for those who teach, study, and do research in geometry and history of mathematics. Cultural historians, physicists, and computer scientists will also find it an important source of information Nota de contenido: History -- The Revolution of János Bolyai -- Gauss and Non-Euclidean Geometry -- János Bolyai’s New Face -- Axiomatical and Logical Aspects -- Hyperbolic Geometry, Dimension-Free -- An Absolute Property of Four Mutually Tangent Circles -- Remembering Donald Coxeter -- Axiomatizations of Hyperbolic and Absolute Geometries -- Logical Axiomatizations of Space-Time. Samples from the Literature -- Polyhedra, Volumes, Discrete Arrangements, Fractals -- Structures in Hyperbolic Space -- The Symmetry of Optimally Dense Packings -- Flexible Octahedra in the Hyperbolic Space -- Fractal Geometry on Hyperbolic Manifolds -- A Volume Formula for Generalised Hyperbolic Tetrahedra -- Tilings, Orbifolds and Manifolds, Visualization -- The Geometry of Hyperbolic Manifolds of Dimension at Least 4 -- Real-Time Animation in Hyperbolic, Spherical, and Product Geometries -- On Spontaneous Surgery on Knots and Links -- Classification of Tile-Transitive 3-Simplex Tilings and Their Realizations in Homogeneous Spaces -- Differential Geometry -- Non-Euclidean Analysis -- Holonomy, Geometry and Topology of Manifolds with Grassmann Structure -- Hypersurfaces of Type Number 2 in the Hyperbolic Four-Space and Their Extensions To Riemannian Geometry -- How Far Does Hyperbolic Geometry Generalize? -- Geometry of the Point Finsler Spaces -- Physics -- Black Hole Perturbations -- Placing the Hyperbolic Geometry of Bolyai and Lobachevsky Centrally in Special Relativity Theory: An Idea Whose Time has Returned En línea: http://dx.doi.org/10.1007/0-387-29555-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34762 Ejemplares
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Título : Physical Applications of Homogeneous Balls Tipo de documento: documento electrónico Autores: Friedman, Yaakov ; SpringerLink (Online service) ; Scarr, Tzvi Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2005 Otro editor: Imprint: Birkhäuser Colección: Progress in Mathematical Physics num. 40 Número de páginas: XXIII, 279 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-8208-8 Idioma : Inglés (eng) Palabras clave: Mathematics Topological groups Lie Applied mathematics Engineering Geometry Differential geometry Physics Gravitation Applications of Mathematical Methods in Classical and Quantum Gravitation, Relativity Theory Groups, Groups Clasificación: 51 Matemáticas Resumen: One of the mathematical challenges of modern physics lies in the development of new tools to efficiently describe different branches of physics within one mathematical framework. This text introduces precisely such a broad mathematical model, one that gives a clear geometric expression of the symmetry of physical laws and is entirely determined by that symmetry. The first three chapters discuss the occurrence of bounded symmetric domains (BSDs) or homogeneous balls and their algebraic structure in physics. It is shown that the set of all possible velocities is a BSD with respect to the projective group; the Lie algebra of this group, expressed as a triple product, defines relativistic dynamics. The particular BSD known as the spin factor is exhibited in two ways: first, as a triple representation of the Canonical Anticommutation Relations, and second, as a ball of symmetric velocities. The associated group is the conformal group, and the triple product on this domain gives a representation of the geometric product defined in Clifford algebras. It is explained why the state space of a two-state quantum mechanical system is the dual space of a spin factor. Ideas from Transmission Line Theory are used to derive the explicit form of the operator Mobius transformations. The book further provides a discussion of how to obtain a triple algebraic structure associated to an arbitrary BSD; the relation between the geometry of the domain and the algebraic structure is explored as well. The last chapter contains a classification of BSDs revealing the connection between the classical and the exceptional domains. With its unifying approach to mathematics and physics, this work will be useful for researchers and graduate students interested in the many physical applications of bounded symmetric domains. It will also benefit a wider audience of mathematicians, physicists, and graduate students working in relativity, geometry, and Lie theory Nota de contenido: 1 Relativity based on symmetry -- 1.1 Space-time transformation based on relativity -- 1.2 Step 6 - Identification of invariants -- 1.3 Relativistic velocity addition -- 1.4 Step 7 - The velocity ball as a bounded symmetric domain -- 1.5 Step 8 - Relativistic dynamics -- 1.6 Notes -- 2 The real spin domain -- 2.1 Symmetric velocity addition -- 2.2 Projective and conformal commutativity and associativity -- 2.3 The Lie group Aut,(Ds) 64 2.3.1 The automorphisms of Ds generated by s-velocity addition -- 2.4 The Lie Algebra autc(Ds) and the spin triple product -- 2.5 Relativistic dynamic equations on Ds -- 2.6 Perpendicular electric and magnetic fields -- 2.7 Notes -- 3 The complex spin factor and applications -- 3.1 The algebraic structure of the complex spin factor -- 3.2 Geometry of the spin factor -- 3.3 The dual space of Sn -- 3.4 The unit ball Ds,n of Sn as a bounded symmetric domain -- 3.5 The Lorentz group representations on Sn -- 3.6 Spin-2 representation in dinv (84) -- 3.7 Summary of the representations of the Lorentz group on S3 and S4 -- 3.8 Notes -- 4 The classical bounded symmetric domains -- 4.1 The classical domains and operators between Hilbert spaces -- 4.2 Classical domains are BSDs -- 4.3 Peirce decomposition in JC*-triples -- 4.4 Non-commutative perturbation -- 4.5 The dual space to a JC*-triple -- 4.6 The infinite-dimensional classical domains -- 4.7 Notes -- 5 The algebraic structure of homogeneous balls -- 5.1 Analytic mappings on Banach spaces -- 5.2 The group Auta (D) -- 5.3 The Lie Algebra of Auta(D) -- 5.4 Algebraic properties of the triple product -- 5.5 Bounded symmetric domains and JB*-triples -- 5.6 The dual of a JB*-triple -- 5.7 Facially symmetric spaces -- 5.8 Notes -- 6 Classification of JBW*-triple factors -- 6.1 Building blocks of atomic JBW*-triples -- 6.2 Methods of gluing quadrangles -- 6.3 Classification of JBW*-triple factors -- 6.4 Structure and representation of JB*-triples -- 6.5 Notes -- References En línea: http://dx.doi.org/10.1007/978-0-8176-8208-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35197 Physical Applications of Homogeneous Balls [documento electrónico] / Friedman, Yaakov ; SpringerLink (Online service) ; Scarr, Tzvi . - Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2005 . - XXIII, 279 p : online resource. - (Progress in Mathematical Physics; 40) .
ISBN : 978-0-8176-8208-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Topological groups Lie Applied mathematics Engineering Geometry Differential geometry Physics Gravitation Applications of Mathematical Methods in Classical and Quantum Gravitation, Relativity Theory Groups, Groups Clasificación: 51 Matemáticas Resumen: One of the mathematical challenges of modern physics lies in the development of new tools to efficiently describe different branches of physics within one mathematical framework. This text introduces precisely such a broad mathematical model, one that gives a clear geometric expression of the symmetry of physical laws and is entirely determined by that symmetry. The first three chapters discuss the occurrence of bounded symmetric domains (BSDs) or homogeneous balls and their algebraic structure in physics. It is shown that the set of all possible velocities is a BSD with respect to the projective group; the Lie algebra of this group, expressed as a triple product, defines relativistic dynamics. The particular BSD known as the spin factor is exhibited in two ways: first, as a triple representation of the Canonical Anticommutation Relations, and second, as a ball of symmetric velocities. The associated group is the conformal group, and the triple product on this domain gives a representation of the geometric product defined in Clifford algebras. It is explained why the state space of a two-state quantum mechanical system is the dual space of a spin factor. Ideas from Transmission Line Theory are used to derive the explicit form of the operator Mobius transformations. The book further provides a discussion of how to obtain a triple algebraic structure associated to an arbitrary BSD; the relation between the geometry of the domain and the algebraic structure is explored as well. The last chapter contains a classification of BSDs revealing the connection between the classical and the exceptional domains. With its unifying approach to mathematics and physics, this work will be useful for researchers and graduate students interested in the many physical applications of bounded symmetric domains. It will also benefit a wider audience of mathematicians, physicists, and graduate students working in relativity, geometry, and Lie theory Nota de contenido: 1 Relativity based on symmetry -- 1.1 Space-time transformation based on relativity -- 1.2 Step 6 - Identification of invariants -- 1.3 Relativistic velocity addition -- 1.4 Step 7 - The velocity ball as a bounded symmetric domain -- 1.5 Step 8 - Relativistic dynamics -- 1.6 Notes -- 2 The real spin domain -- 2.1 Symmetric velocity addition -- 2.2 Projective and conformal commutativity and associativity -- 2.3 The Lie group Aut,(Ds) 64 2.3.1 The automorphisms of Ds generated by s-velocity addition -- 2.4 The Lie Algebra autc(Ds) and the spin triple product -- 2.5 Relativistic dynamic equations on Ds -- 2.6 Perpendicular electric and magnetic fields -- 2.7 Notes -- 3 The complex spin factor and applications -- 3.1 The algebraic structure of the complex spin factor -- 3.2 Geometry of the spin factor -- 3.3 The dual space of Sn -- 3.4 The unit ball Ds,n of Sn as a bounded symmetric domain -- 3.5 The Lorentz group representations on Sn -- 3.6 Spin-2 representation in dinv (84) -- 3.7 Summary of the representations of the Lorentz group on S3 and S4 -- 3.8 Notes -- 4 The classical bounded symmetric domains -- 4.1 The classical domains and operators between Hilbert spaces -- 4.2 Classical domains are BSDs -- 4.3 Peirce decomposition in JC*-triples -- 4.4 Non-commutative perturbation -- 4.5 The dual space to a JC*-triple -- 4.6 The infinite-dimensional classical domains -- 4.7 Notes -- 5 The algebraic structure of homogeneous balls -- 5.1 Analytic mappings on Banach spaces -- 5.2 The group Auta (D) -- 5.3 The Lie Algebra of Auta(D) -- 5.4 Algebraic properties of the triple product -- 5.5 Bounded symmetric domains and JB*-triples -- 5.6 The dual of a JB*-triple -- 5.7 Facially symmetric spaces -- 5.8 Notes -- 6 Classification of JBW*-triple factors -- 6.1 Building blocks of atomic JBW*-triples -- 6.2 Methods of gluing quadrangles -- 6.3 Classification of JBW*-triple factors -- 6.4 Structure and representation of JB*-triples -- 6.5 Notes -- References En línea: http://dx.doi.org/10.1007/978-0-8176-8208-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35197 Ejemplares
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