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Título : Einstein and the Changing Worldviews of Physics Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Christoph Lehner ; 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) ; Christoph Lehner ; 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 : From Hyperbolic Systems to Kinetic Theory : A Personalized Quest Tipo de documento: documento electrónico Autores: Tartar, Luc ; SpringerLink (Online service) Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2008 Colección: Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113 num. 6 Número de páginas: XXVIII, 282 p Il.: online resource ISBN/ISSN/DL: 978-3-540-77562-1 Idioma : Inglés (eng) Palabras clave: Mathematics Dynamics Ergodic theory Partial differential equations Physics Continuum physics Differential Equations Classical Mathematical Methods in Dynamical Systems and Theory Clasificación: 51 Matemáticas Resumen: Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from Poincaré's theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity! Nota de contenido: Historical Perspective -- Hyperbolic Systems: Riemann Invariants, Rarefaction Waves -- Hyperbolic Systems: Contact Discontinuities, Shocks -- The Burgers Equation and the 1-D Scalar Case -- The 1-D Scalar Case: the E-Conditions of Lax and of Oleinik -- Hopf's Formulation of the E-Condition of Oleinik -- The Burgers Equation: Special Solutions -- The Burgers Equation: Small Perturbations; the Heat Equation -- Fourier Transform; the Asymptotic Behaviour for the Heat Equation -- Radon Measures; the Law of Large Numbers -- A 1-D Model with Characteristic Speed 1/? -- A 2-D Generalization; the Perron–Frobenius Theory -- A General Finite-Dimensional Model with Characteristic Speed 1/? -- Discrete Velocity Models -- The Mimura–Nishida and the Crandall–Tartar Existence Theorems -- Systems Satisfying My Condition (S) -- Asymptotic Estimates for the Broadwell and the Carleman Models -- Oscillating Solutions; the 2-D Broadwell Model -- Oscillating Solutions: the Carleman Model -- The Carleman Model: Asymptotic Behaviour -- Oscillating Solutions: the Broadwell Model -- Generalized Invariant Regions; the Varadhan Estimate -- Questioning Physics; from Classical Particles to Balance Laws -- Balance Laws; What Are Forces? -- D. Bernoulli: from Masslets and Springs to the 1-D Wave Equation -- Cauchy: from Masslets and Springs to 2-D Linearized Elasticity -- The Two-Body Problem -- The Boltzmann Equation -- The Illner–Shinbrot and the Hamdache Existence Theorems -- The Hilbert Expansion -- Compactness by Integration -- Wave Front Sets; H-Measures -- H-Measures and “Idealized Particles” -- Variants of H-Measures -- Biographical Information -- Abbreviations and Mathematical Notation En línea: http://dx.doi.org/10.1007/978-3-540-77562-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34371 From Hyperbolic Systems to Kinetic Theory : A Personalized Quest [documento electrónico] / Tartar, Luc ; SpringerLink (Online service) . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2008 . - XXVIII, 282 p : online resource. - (Lecture Notes of the Unione Matematica Italiana, ISSN 1862-9113; 6) .
ISBN : 978-3-540-77562-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Dynamics Ergodic theory Partial differential equations Physics Continuum physics Differential Equations Classical Mathematical Methods in Dynamical Systems and Theory Clasificación: 51 Matemáticas Resumen: Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from Poincaré's theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity! Nota de contenido: Historical Perspective -- Hyperbolic Systems: Riemann Invariants, Rarefaction Waves -- Hyperbolic Systems: Contact Discontinuities, Shocks -- The Burgers Equation and the 1-D Scalar Case -- The 1-D Scalar Case: the E-Conditions of Lax and of Oleinik -- Hopf's Formulation of the E-Condition of Oleinik -- The Burgers Equation: Special Solutions -- The Burgers Equation: Small Perturbations; the Heat Equation -- Fourier Transform; the Asymptotic Behaviour for the Heat Equation -- Radon Measures; the Law of Large Numbers -- A 1-D Model with Characteristic Speed 1/? -- A 2-D Generalization; the Perron–Frobenius Theory -- A General Finite-Dimensional Model with Characteristic Speed 1/? -- Discrete Velocity Models -- The Mimura–Nishida and the Crandall–Tartar Existence Theorems -- Systems Satisfying My Condition (S) -- Asymptotic Estimates for the Broadwell and the Carleman Models -- Oscillating Solutions; the 2-D Broadwell Model -- Oscillating Solutions: the Carleman Model -- The Carleman Model: Asymptotic Behaviour -- Oscillating Solutions: the Broadwell Model -- Generalized Invariant Regions; the Varadhan Estimate -- Questioning Physics; from Classical Particles to Balance Laws -- Balance Laws; What Are Forces? -- D. Bernoulli: from Masslets and Springs to the 1-D Wave Equation -- Cauchy: from Masslets and Springs to 2-D Linearized Elasticity -- The Two-Body Problem -- The Boltzmann Equation -- The Illner–Shinbrot and the Hamdache Existence Theorems -- The Hilbert Expansion -- Compactness by Integration -- Wave Front Sets; H-Measures -- H-Measures and “Idealized Particles” -- Variants of H-Measures -- Biographical Information -- Abbreviations and Mathematical Notation En línea: http://dx.doi.org/10.1007/978-3-540-77562-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34371 Ejemplares
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Título : Introduction to Analytical Dynamics : Revised Edition Tipo de documento: documento electrónico Autores: Nicholas Michael John Woodhouse ; SpringerLink (Online service) Editorial: London : Springer London Fecha de publicación: 2009 Colección: Springer Undergraduate Mathematics Series, ISSN 1615-2085 Número de páginas: XIII, 240 p. 42 illus Il.: online resource ISBN/ISSN/DL: 978-1-84882-816-2 Idioma : Inglés (eng) Palabras clave: Physics Applied mathematics Engineering Continuum physics Mechanics Mechanics, Theoretical, Mathematical and Computational Classical Applications of Mathematics Theoretical Clasificación: 51 Matemáticas Resumen: Analytical dynamics forms an important part of any undergraduate programme in applied mathematics and physics: it develops intuition about three-dimensional space and provides invaluable practice in problem solving. First published in 1987, this text is an introduction to the core ideas. It offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton’s laws through Lagrange’s equations and Hamilton’s principle, to Hamilton’s equations and canonical transformations. This new edition has been extensively revised and updated to include: A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations. A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles. A greater emphasis on the links to special relativity and quantum theory, e.g., linking Schrödinger’s equation to Hamilton-Jacobi theory, showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics. Aimed at second- and third-year undergraduates, the book assumes some familiarity with elementary linear algebra, the chain rule for partial derivatives, and vector mechanics in three dimensions, although the latter is not essential. A wealth of examples show the subject in action and a range of exercises – with solutions – are provided to help test understanding Nota de contenido: Frames of Reference -- One Degree of Freedom -- Lagrangian Mechanics -- Noether#x2019;s Theorem -- Rigid Bodies -- Oscillations -- Hamiltonian Mechanics -- Geometry of Classical Mechanics -- Epilogue: Relativity and Quantum Theory En línea: http://dx.doi.org/10.1007/978-1-84882-816-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33988 Introduction to Analytical Dynamics : Revised Edition [documento electrónico] / Nicholas Michael John Woodhouse ; SpringerLink (Online service) . - London : Springer London, 2009 . - XIII, 240 p. 42 illus : online resource. - (Springer Undergraduate Mathematics Series, ISSN 1615-2085) .
ISBN : 978-1-84882-816-2
Idioma : Inglés (eng)
Palabras clave: Physics Applied mathematics Engineering Continuum physics Mechanics Mechanics, Theoretical, Mathematical and Computational Classical Applications of Mathematics Theoretical Clasificación: 51 Matemáticas Resumen: Analytical dynamics forms an important part of any undergraduate programme in applied mathematics and physics: it develops intuition about three-dimensional space and provides invaluable practice in problem solving. First published in 1987, this text is an introduction to the core ideas. It offers concise but clear explanations and derivations to give readers a confident grasp of the chain of argument that leads from Newton’s laws through Lagrange’s equations and Hamilton’s principle, to Hamilton’s equations and canonical transformations. This new edition has been extensively revised and updated to include: A chapter on symplectic geometry and the geometric interpretation of some of the coordinate calculations. A more systematic treatment of the conections with the phase-plane analysis of ODEs; and an improved treatment of Euler angles. A greater emphasis on the links to special relativity and quantum theory, e.g., linking Schrödinger’s equation to Hamilton-Jacobi theory, showing how ideas from this classical subject link into contemporary areas of mathematics and theoretical physics. Aimed at second- and third-year undergraduates, the book assumes some familiarity with elementary linear algebra, the chain rule for partial derivatives, and vector mechanics in three dimensions, although the latter is not essential. A wealth of examples show the subject in action and a range of exercises – with solutions – are provided to help test understanding Nota de contenido: Frames of Reference -- One Degree of Freedom -- Lagrangian Mechanics -- Noether#x2019;s Theorem -- Rigid Bodies -- Oscillations -- Hamiltonian Mechanics -- Geometry of Classical Mechanics -- Epilogue: Relativity and Quantum Theory En línea: http://dx.doi.org/10.1007/978-1-84882-816-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33988 Ejemplares
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Título : Multiscale Modeling and Simulation in Science Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Björn Engquist ; Per Lötstedt ; Runborg, Olof Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2009 Colección: Lecture Notes in Computational Science and Engineering, ISSN 1439-7358 num. 66 Número de páginas: XIV, 320 p Il.: online resource ISBN/ISSN/DL: 978-3-540-88857-4 Idioma : Inglés (eng) Palabras clave: Mathematics Chemistry, Physical and theoretical Computer mathematics Physics Continuum physics Astrophysics Computational Science Engineering Numerical Analysis Classical Astroparticles Theoretical Chemistry Clasificación: 51 Matemáticas Resumen: This book contains lecture notes of current development in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, fast multipole methods and wavelets. The text includes well designed exercises and project reports on different applications such as astrophysics, computational chemistry, porous media flow and climate change Nota de contenido: Tutorials -- Multiscale Methods for Subsurface Flow -- Multiscale Modelling of Complex Fluids: A Mathematical Initiation -- Fast Algorithms for Boundary Integral Equations -- Wavelets andWavelet Based Numerical Homogenization -- Multiscale Computations for Highly Oscillatory Problems -- Projects -- Quantum Mechanics/Classical Mechanics Modeling of Biological Systems -- Multiple Scales in Solid State Physics -- Climate Sensitivity and Variability Examined in a Global Climate Model -- Coarse-scale Modeling of Flow in Gas-injection Processes for Enhanced Oil Recovery -- Photo-Ionization Dynamics Simulation -- Time Scales in Molecular Reaction Dynamics -- Complex Band Structures of Spintronics Materials En línea: http://dx.doi.org/10.1007/978-3-540-88857-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34046 Multiscale Modeling and Simulation in Science [documento electrónico] / SpringerLink (Online service) ; Björn Engquist ; Per Lötstedt ; Runborg, Olof . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2009 . - XIV, 320 p : online resource. - (Lecture Notes in Computational Science and Engineering, ISSN 1439-7358; 66) .
ISBN : 978-3-540-88857-4
Idioma : Inglés (eng)
Palabras clave: Mathematics Chemistry, Physical and theoretical Computer mathematics Physics Continuum physics Astrophysics Computational Science Engineering Numerical Analysis Classical Astroparticles Theoretical Chemistry Clasificación: 51 Matemáticas Resumen: This book contains lecture notes of current development in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, fast multipole methods and wavelets. The text includes well designed exercises and project reports on different applications such as astrophysics, computational chemistry, porous media flow and climate change Nota de contenido: Tutorials -- Multiscale Methods for Subsurface Flow -- Multiscale Modelling of Complex Fluids: A Mathematical Initiation -- Fast Algorithms for Boundary Integral Equations -- Wavelets andWavelet Based Numerical Homogenization -- Multiscale Computations for Highly Oscillatory Problems -- Projects -- Quantum Mechanics/Classical Mechanics Modeling of Biological Systems -- Multiple Scales in Solid State Physics -- Climate Sensitivity and Variability Examined in a Global Climate Model -- Coarse-scale Modeling of Flow in Gas-injection Processes for Enhanced Oil Recovery -- Photo-Ionization Dynamics Simulation -- Time Scales in Molecular Reaction Dynamics -- Complex Band Structures of Spintronics Materials En línea: http://dx.doi.org/10.1007/978-3-540-88857-4 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34046 Ejemplares
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Título : Physical Applications of Homogeneous Balls Tipo de documento: documento electrónico Autores: Yaakov Friedman ; 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] / Yaakov Friedman ; 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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