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Autor Naber, Gregory L |
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Título : The Geometry of Minkowski Spacetime : An Introduction to the Mathematics of the Special Theory of Relativity Tipo de documento: documento electrónico Autores: Naber, Gregory L ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2012 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 92 Número de páginas: XVI, 324 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7838-7 Idioma : Inglés (eng) Palabras clave: Mathematics Manifolds (Mathematics) Complex manifolds Physics Gravitation and Cell Complexes (incl. Diff.Topology) Classical Quantum Gravitation, Relativity Theory Mathematical Methods in Clasificación: 51 Matemáticas Resumen: This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman’s characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac’s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology. The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title. Reviews of first edition: “… a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics.” (American Mathematical Society, 1993) “Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations.” (CHOICE, 1993) “… his talent in choosing the most significant results and ordering them within the book can’t be denied. The reading of the book is, really, a pleasure.” (Dutch Mathematical Society, 1993) En línea: http://dx.doi.org/10.1007/978-1-4419-7838-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32710 The Geometry of Minkowski Spacetime : An Introduction to the Mathematics of the Special Theory of Relativity [documento electrónico] / Naber, Gregory L ; SpringerLink (Online service) . - New York, NY : Springer New York, 2012 . - XVI, 324 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 92) .
ISBN : 978-1-4419-7838-7
Idioma : Inglés (eng)
Palabras clave: Mathematics Manifolds (Mathematics) Complex manifolds Physics Gravitation and Cell Complexes (incl. Diff.Topology) Classical Quantum Gravitation, Relativity Theory Mathematical Methods in Clasificación: 51 Matemáticas Resumen: This book offers a presentation of the special theory of relativity that is mathematically rigorous and yet spells out in considerable detail the physical significance of the mathematics. It treats, in addition to the usual menu of topics one is accustomed to finding in introductions to special relativity, a wide variety of results of more contemporary origin. These include Zeeman’s characterization of the causal automorphisms of Minkowski spacetime, the Penrose theorem on the apparent shape of a relativistically moving sphere, a detailed introduction to the theory of spinors, a Petrov-type classification of electromagnetic fields in both tensor and spinor form, a topology for Minkowski spacetime whose homeomorphism group is essentially the Lorentz group, and a careful discussion of Dirac’s famous Scissors Problem and its relation to the notion of a two-valued representation of the Lorentz group. This second edition includes a new chapter on the de Sitter universe which is intended to serve two purposes. The first is to provide a gentle prologue to the steps one must take to move beyond special relativity and adapt to the presence of gravitational fields that cannot be considered negligible. The second is to understand some of the basic features of a model of the empty universe that differs markedly from Minkowski spacetime, but may be recommended by recent astronomical observations suggesting that the expansion of our own universe is accelerating rather than slowing down. The treatment presumes only a knowledge of linear algebra in the first three chapters, a bit of real analysis in the fourth and, in two appendices, some elementary point-set topology. The first edition of the book received the 1993 CHOICE award for Outstanding Academic Title. Reviews of first edition: “… a valuable contribution to the pedagogical literature which will be enjoyed by all who delight in precise mathematics and physics.” (American Mathematical Society, 1993) “Where many physics texts explain physical phenomena by means of mathematical models, here a rigorous and detailed mathematical development is accompanied by precise physical interpretations.” (CHOICE, 1993) “… his talent in choosing the most significant results and ordering them within the book can’t be denied. The reading of the book is, really, a pleasure.” (Dutch Mathematical Society, 1993) En línea: http://dx.doi.org/10.1007/978-1-4419-7838-7 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=32710 Ejemplares
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Título : Topology, Geometry and Gauge fields : Foundations Tipo de documento: documento electrónico Autores: Naber, Gregory L ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Otro editor: Imprint: Springer Colección: Texts in Applied Mathematics, ISSN 0939-2475 num. 25 Número de páginas: XX, 437 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7254-5 Idioma : Inglés (eng) Palabras clave: Mathematics Geometry Topology Elementary particles (Physics) Quantum field theory Particles, Field Theory Clasificación: 51 Matemáticas Resumen: This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author’s point of view is that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The goal is to weave together rudimentary notions from the classical gauge theories of physics and the topological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, and a solid background in real analysis and linear algebra with some of the vocabulary of modern algebra. To such a reader we offer an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2)-connections on S4 with instanton number -1. This second edition of the book includes a new chapter on singular homology theory and a new appendix outlining Donaldson’s beautiful application of gauge theory to the topology of compact, simply connected , smooth 4-manifolds with definite intersection form. Reviews of the first edition: “It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics…Naber combines a deep knowledge of his subject with an excellent informal writing style.” (NZMS Newsletter) "...this book should be very interesting for mathematicians and physicists (as well as other scientists) who are concerned with gauge theories." (ZENTRALBLATT FUER MATHEMATIK) “The book is well written and the examples do a great service to the reader. It will be a helpful companion to anyone teaching or studying gauge theory …” (Mathematical Reviews) Nota de contenido: Contents: Preface -- Physical and geometrical motivation 1 Topological spaces -- Homotopy groups -- Principal bundles -- Differentiable manifolds and matrix Lie groups -- Gauge fields and Instantons. Appendix. References. Index En línea: http://dx.doi.org/10.1007/978-1-4419-7254-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33158 Topology, Geometry and Gauge fields : Foundations [documento electrónico] / Naber, Gregory L ; SpringerLink (Online service) . - New York, NY : Springer New York : Imprint: Springer, 2011 . - XX, 437 p : online resource. - (Texts in Applied Mathematics, ISSN 0939-2475; 25) .
ISBN : 978-1-4419-7254-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Geometry Topology Elementary particles (Physics) Quantum field theory Particles, Field Theory Clasificación: 51 Matemáticas Resumen: This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author’s point of view is that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The goal is to weave together rudimentary notions from the classical gauge theories of physics and the topological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, and a solid background in real analysis and linear algebra with some of the vocabulary of modern algebra. To such a reader we offer an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2)-connections on S4 with instanton number -1. This second edition of the book includes a new chapter on singular homology theory and a new appendix outlining Donaldson’s beautiful application of gauge theory to the topology of compact, simply connected , smooth 4-manifolds with definite intersection form. Reviews of the first edition: “It is unusual to find a book so carefully tailored to the needs of this interdisciplinary area of mathematical physics…Naber combines a deep knowledge of his subject with an excellent informal writing style.” (NZMS Newsletter) "...this book should be very interesting for mathematicians and physicists (as well as other scientists) who are concerned with gauge theories." (ZENTRALBLATT FUER MATHEMATIK) “The book is well written and the examples do a great service to the reader. It will be a helpful companion to anyone teaching or studying gauge theory …” (Mathematical Reviews) Nota de contenido: Contents: Preface -- Physical and geometrical motivation 1 Topological spaces -- Homotopy groups -- Principal bundles -- Differentiable manifolds and matrix Lie groups -- Gauge fields and Instantons. Appendix. References. Index En línea: http://dx.doi.org/10.1007/978-1-4419-7254-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33158 Ejemplares
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Título : Topology, Geometry and Gauge fields : Interactions Tipo de documento: documento electrónico Autores: Naber, Gregory L ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2011 Colección: Applied Mathematical Sciences, ISSN 0066-5452 num. 141 Número de páginas: XII, 420 p Il.: online resource ISBN/ISSN/DL: 978-1-4419-7895-0 Idioma : Inglés (eng) Palabras clave: Mathematics Geometry Combinatorics Physics Theoretical, Mathematical and Computational Clasificación: 51 Matemáticas Resumen: This volume is intended to carry on the program, initiated in Topology, Geometry, and Gauge Fields: Foundations (Springer, 2010), of exploring the interrelations between particle physics and topology that arise from their shared notion of a gauge field. The text begins with a synopsis of the geometrical background assumed of the reader (manifolds, Lie groups, bundles, connections, etc.). There follows a lengthy, and somewhat informal discussion of a number of the most basic of the classical gauge theories arising in physics, including classical electromagnetic theory and Dirac monopoles, the Klein-Gordon and Dirac equations and SU(2) Yang-Mills-Higgs theory. The real purpose here is to witness such things as spacetime manifolds, spinor structures, de Rham cohomology, and Chern classes arise of their own accord in meaningful physics. All of these are then developed rigorously in the remaining chapters. With the precise definitions in hand, one can, for example, fully identify magnetic charge and instanton number with the Chern numbers of the bundles on which the charge and instanton live, and uncover the obstruction to the existence of a spinor structure in the form of the second Stiefel-Whitney class. This second edition of the book includes, in an Appendix, a much expanded sketch of Seiberg-Witten gauge theory, including a brief discussion of its origins in physics and its implications for topology. To provide the reader with the opportunity to pause en route and join in the fun, there are 228 exercises, each an integral part of the development and each located at precisely the point at which it can be solved with optimal benefit. Reviews of first edition: “Naber’s goal is not to teach a sterile course on geometry and topology, but rather to enable us to see the subject in action, through gauge theory.” (SIAM Review) “The presentation … is enriched by detailed discussions about the physical interpretations of connections, their curvatures and characteristic classes. I particularly enjoyed Chapter 2 where many fundamental physical examples are discussed at great length in a reader friendly fashion. No detail is left to the reader’s imagination or interpretation. I am not aware of another source where these very important examples and ideas are presented at a level accessible to beginners.” (Mathematical Reviews) Nota de contenido: Preface -- Acknowledgements -- Geometrical Background -- Physical Motivation -- Frame Bundles and Spacetime -- Differential Forms and Integration Introduction -- de Rham Cohomology Introduction -- Characteristic Classes -- Appendix -- References -- Symbols -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-7895-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33174 Topology, Geometry and Gauge fields : Interactions [documento electrónico] / Naber, Gregory L ; SpringerLink (Online service) . - New York, NY : Springer New York, 2011 . - XII, 420 p : online resource. - (Applied Mathematical Sciences, ISSN 0066-5452; 141) .
ISBN : 978-1-4419-7895-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Geometry Combinatorics Physics Theoretical, Mathematical and Computational Clasificación: 51 Matemáticas Resumen: This volume is intended to carry on the program, initiated in Topology, Geometry, and Gauge Fields: Foundations (Springer, 2010), of exploring the interrelations between particle physics and topology that arise from their shared notion of a gauge field. The text begins with a synopsis of the geometrical background assumed of the reader (manifolds, Lie groups, bundles, connections, etc.). There follows a lengthy, and somewhat informal discussion of a number of the most basic of the classical gauge theories arising in physics, including classical electromagnetic theory and Dirac monopoles, the Klein-Gordon and Dirac equations and SU(2) Yang-Mills-Higgs theory. The real purpose here is to witness such things as spacetime manifolds, spinor structures, de Rham cohomology, and Chern classes arise of their own accord in meaningful physics. All of these are then developed rigorously in the remaining chapters. With the precise definitions in hand, one can, for example, fully identify magnetic charge and instanton number with the Chern numbers of the bundles on which the charge and instanton live, and uncover the obstruction to the existence of a spinor structure in the form of the second Stiefel-Whitney class. This second edition of the book includes, in an Appendix, a much expanded sketch of Seiberg-Witten gauge theory, including a brief discussion of its origins in physics and its implications for topology. To provide the reader with the opportunity to pause en route and join in the fun, there are 228 exercises, each an integral part of the development and each located at precisely the point at which it can be solved with optimal benefit. Reviews of first edition: “Naber’s goal is not to teach a sterile course on geometry and topology, but rather to enable us to see the subject in action, through gauge theory.” (SIAM Review) “The presentation … is enriched by detailed discussions about the physical interpretations of connections, their curvatures and characteristic classes. I particularly enjoyed Chapter 2 where many fundamental physical examples are discussed at great length in a reader friendly fashion. No detail is left to the reader’s imagination or interpretation. I am not aware of another source where these very important examples and ideas are presented at a level accessible to beginners.” (Mathematical Reviews) Nota de contenido: Preface -- Acknowledgements -- Geometrical Background -- Physical Motivation -- Frame Bundles and Spacetime -- Differential Forms and Integration Introduction -- de Rham Cohomology Introduction -- Characteristic Classes -- Appendix -- References -- Symbols -- Index En línea: http://dx.doi.org/10.1007/978-1-4419-7895-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33174 Ejemplares
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