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Título : Modern Differential Geometry in Gauge Theories : Maxwell Fields, Volume I Tipo de documento: documento electrónico Autores: Mallios, Anastasios ; SpringerLink (Online service) Editorial: Boston, MA : Birkhäuser Boston Fecha de publicación: 2006 Número de páginas: XVII, 293 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4474-1 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Field theory (Physics) Global analysis (Mathematics) Manifolds Differential geometry Physics Optics Electrodynamics Elementary particles Quantum field Geometry Mathematical Methods in Theory and Polynomials Particles, Analysis on Clasificación: 51 Matemáticas Resumen: Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications. Modern Differential Geometry in Gauge Theories is a two-volume research monograph that systematically applies a sheaf-theoretic approach to such physical theories as gauge theory. Beginning with Volume 1, the focus is on Maxwell fields. All the basic concepts of this mathematical approach are formulated and used thereafter to describe elementary particles, electromagnetism, and geometric prequantization. Maxwell fields are fully examined and classified in the language of sheaf theory and sheaf cohomology. Continuing in Volume 2, this sheaf-theoretic approach is applied to Yang–Mills fields in general. The text contains a wealth of detailed and rigorous computations and will appeal to mathematicians and physicists, along with advanced undergraduate and graduate students, interested in applications of differential geometry to physical theories such as general relativity, elementary particle physics and quantum gravity Nota de contenido: Maxwell Fields: General Theory -- The Rudiments of Abstract Differential Geometry -- Elementary Particles: Sheaf-Theoretic Classification, by Spin-Structure, According to Selesnick’s Correspondence Principle -- Electromagnetism -- Cohomological Classification of Maxwell and Hermitian Maxwell Fields -- Geometric Prequantization En línea: http://dx.doi.org/10.1007/0-8176-4474-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34865 Modern Differential Geometry in Gauge Theories : Maxwell Fields, Volume I [documento electrónico] / Mallios, Anastasios ; SpringerLink (Online service) . - Boston, MA : Birkhäuser Boston, 2006 . - XVII, 293 p : online resource.
ISBN : 978-0-8176-4474-1
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Field theory (Physics) Global analysis (Mathematics) Manifolds Differential geometry Physics Optics Electrodynamics Elementary particles Quantum field Geometry Mathematical Methods in Theory and Polynomials Particles, Analysis on Clasificación: 51 Matemáticas Resumen: Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications. Modern Differential Geometry in Gauge Theories is a two-volume research monograph that systematically applies a sheaf-theoretic approach to such physical theories as gauge theory. Beginning with Volume 1, the focus is on Maxwell fields. All the basic concepts of this mathematical approach are formulated and used thereafter to describe elementary particles, electromagnetism, and geometric prequantization. Maxwell fields are fully examined and classified in the language of sheaf theory and sheaf cohomology. Continuing in Volume 2, this sheaf-theoretic approach is applied to Yang–Mills fields in general. The text contains a wealth of detailed and rigorous computations and will appeal to mathematicians and physicists, along with advanced undergraduate and graduate students, interested in applications of differential geometry to physical theories such as general relativity, elementary particle physics and quantum gravity Nota de contenido: Maxwell Fields: General Theory -- The Rudiments of Abstract Differential Geometry -- Elementary Particles: Sheaf-Theoretic Classification, by Spin-Structure, According to Selesnick’s Correspondence Principle -- Electromagnetism -- Cohomological Classification of Maxwell and Hermitian Maxwell Fields -- Geometric Prequantization En línea: http://dx.doi.org/10.1007/0-8176-4474-1 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34865 Ejemplares
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Título : Modern Differential Geometry in Gauge Theories : Yang¿Mills Fields, Volume II Tipo de documento: documento electrónico Autores: Mallios, Anastasios ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2010 Número de páginas: XIX, 234 p. 5 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4634-9 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Field theory (Physics) Global analysis (Mathematics) Manifolds Differential geometry Physics Optics Electrodynamics Elementary particles Quantum field Geometry Mathematical Methods in Theory and Polynomials Particles, Analysis on Clasificación: 51 Matemáticas Resumen: Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications. Modern Differential Geometry in Gauge Theories is a two-volume research monograph that systematically applies a sheaf-theoretic approach to such physical theories as gauge theory. Beginning with Volume 1, the focus is on Maxwell fields. All the basic concepts of this mathematical approach are formulated and used thereafter to describe elementary particles, electromagnetism, and geometric prequantization. Maxwell fields are fully examined and classified in the language of sheaf theory and sheaf cohomology. Continuing in Volume 2, this sheaf-theoretic approach is applied to Yang–Mills fields in general. The text contains a wealth of detailed and rigorous computations and will appeal to mathematicians and physicists, along with advanced undergraduate and graduate students, interested in applications of differential geometry to physical theories such as general relativity, elementary particle physics and quantum gravity Nota de contenido: Yang–Mills Theory:General Theory -- Abstract Yang#x2013;Mills Theory -- Moduli Spaces of -Connections of Yang#x2013;Mills Fields -- Geometry of Yang#x2013;Mills -Connections -- General Relativity -- General Relativity, as a Gauge Theory. Singularities En línea: http://dx.doi.org/10.1007/978-0-8176-4634-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33534 Modern Differential Geometry in Gauge Theories : Yang¿Mills Fields, Volume II [documento electrónico] / Mallios, Anastasios ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2010 . - XIX, 234 p. 5 illus : online resource.
ISBN : 978-0-8176-4634-9
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Field theory (Physics) Global analysis (Mathematics) Manifolds Differential geometry Physics Optics Electrodynamics Elementary particles Quantum field Geometry Mathematical Methods in Theory and Polynomials Particles, Analysis on Clasificación: 51 Matemáticas Resumen: Differential geometry, in the classical sense, is developed through the theory of smooth manifolds. Modern differential geometry from the author’s perspective is used in this work to describe physical theories of a geometric character without using any notion of calculus (smoothness). Instead, an axiomatic treatment of differential geometry is presented via sheaf theory (geometry) and sheaf cohomology (analysis). Using vector sheaves, in place of bundles, based on arbitrary topological spaces, this unique approach in general furthers new perspectives and calculations that generate unexpected potential applications. Modern Differential Geometry in Gauge Theories is a two-volume research monograph that systematically applies a sheaf-theoretic approach to such physical theories as gauge theory. Beginning with Volume 1, the focus is on Maxwell fields. All the basic concepts of this mathematical approach are formulated and used thereafter to describe elementary particles, electromagnetism, and geometric prequantization. Maxwell fields are fully examined and classified in the language of sheaf theory and sheaf cohomology. Continuing in Volume 2, this sheaf-theoretic approach is applied to Yang–Mills fields in general. The text contains a wealth of detailed and rigorous computations and will appeal to mathematicians and physicists, along with advanced undergraduate and graduate students, interested in applications of differential geometry to physical theories such as general relativity, elementary particle physics and quantum gravity Nota de contenido: Yang–Mills Theory:General Theory -- Abstract Yang#x2013;Mills Theory -- Moduli Spaces of -Connections of Yang#x2013;Mills Fields -- Geometry of Yang#x2013;Mills -Connections -- General Relativity -- General Relativity, as a Gauge Theory. Singularities En línea: http://dx.doi.org/10.1007/978-0-8176-4634-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33534 Ejemplares
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Título : The Versatile Soliton Tipo de documento: documento electrónico Autores: Filippov, Alexandre T ; SpringerLink (Online service) Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2010 Colección: Modern Birkhäuser Classics Número de páginas: XVII, 261 p. 77 illus Il.: online resource ISBN/ISSN/DL: 978-0-8176-4974-6 Idioma : Inglés (eng) Palabras clave: Mathematics Applied mathematics Engineering Physics Elementary particles (Physics) Quantum field theory Applications of Theoretical, Mathematical and Computational Particles, Field Theory Clasificación: 51 Matemáticas Resumen: The soliton, a solitary wave impulse preserving its shape and strikingly similar to a particle, is one of the most fascinating and beautiful phenomena in the physics of nonlinear waves. In this classic book, the concept of the soliton is traced from the beginning of the last century to modern times, with recent applications in biology, oceanography, solid state physics, electronics, elementary particle physics, and cosmology. The Versatile Soliton is an appropriate title indeed. There is much new historical information in the book…The book is written in a lively language and the physics presented in a clear, pedagogical style. Most of the chapters require only knowledge of fairly elementary mathematics and the main ideas of soliton physics are well explained without mathematics at all…Yet it contains valuable information and offers a historical review of soliton physics that cannot be found elsewhere. —Centaurus In summary, this book is a good elementary treatment of solitons and the related history of physics and mathematics, even for readers with little knowledge of advanced mathematics. For readers with the latter knowledge, it is still a good introduction to the physical ideas required for the understanding of solitons prior to the study of more mathematical treatments from other sources. —Mathematical Reviews This engaging book is an excellent introduction into the wonderful world of soliton mechanics. —Zentralblatt Math No doubt, everyone can get new information from the book. First, the book is strongly recommended to young researchers. In a certain sense, the book is unique and definitely will find a niche among numerous textbooks on solitons. —Physicala Nota de contenido: An Early History of the Soliton -- A Century and a Half Ago -- The Great Solitary Wave of John Scott Russell -- Relatives of the Soliton -- Nonlinear Oscillations and Waves -- A Portrait of the Pendulum -- From Pendulum to Waves and Solitons -- The Present and Future of the Soliton -- Frenkel’s Solitons -- Rebirth of the Soliton -- Modern Solitons En línea: http://dx.doi.org/10.1007/978-0-8176-4974-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33563 The Versatile Soliton [documento electrónico] / Filippov, Alexandre T ; SpringerLink (Online service) . - Boston : Birkhäuser Boston, 2010 . - XVII, 261 p. 77 illus : online resource. - (Modern Birkhäuser Classics) .
ISBN : 978-0-8176-4974-6
Idioma : Inglés (eng)
Palabras clave: Mathematics Applied mathematics Engineering Physics Elementary particles (Physics) Quantum field theory Applications of Theoretical, Mathematical and Computational Particles, Field Theory Clasificación: 51 Matemáticas Resumen: The soliton, a solitary wave impulse preserving its shape and strikingly similar to a particle, is one of the most fascinating and beautiful phenomena in the physics of nonlinear waves. In this classic book, the concept of the soliton is traced from the beginning of the last century to modern times, with recent applications in biology, oceanography, solid state physics, electronics, elementary particle physics, and cosmology. The Versatile Soliton is an appropriate title indeed. There is much new historical information in the book…The book is written in a lively language and the physics presented in a clear, pedagogical style. Most of the chapters require only knowledge of fairly elementary mathematics and the main ideas of soliton physics are well explained without mathematics at all…Yet it contains valuable information and offers a historical review of soliton physics that cannot be found elsewhere. —Centaurus In summary, this book is a good elementary treatment of solitons and the related history of physics and mathematics, even for readers with little knowledge of advanced mathematics. For readers with the latter knowledge, it is still a good introduction to the physical ideas required for the understanding of solitons prior to the study of more mathematical treatments from other sources. —Mathematical Reviews This engaging book is an excellent introduction into the wonderful world of soliton mechanics. —Zentralblatt Math No doubt, everyone can get new information from the book. First, the book is strongly recommended to young researchers. In a certain sense, the book is unique and definitely will find a niche among numerous textbooks on solitons. —Physicala Nota de contenido: An Early History of the Soliton -- A Century and a Half Ago -- The Great Solitary Wave of John Scott Russell -- Relatives of the Soliton -- Nonlinear Oscillations and Waves -- A Portrait of the Pendulum -- From Pendulum to Waves and Solitons -- The Present and Future of the Soliton -- Frenkel’s Solitons -- Rebirth of the Soliton -- Modern Solitons En línea: http://dx.doi.org/10.1007/978-0-8176-4974-6 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33563 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 : Global Propagation of Regular Nonlinear Hyperbolic Waves Tipo de documento: documento electrónico Autores: Tatsien, Li ; SpringerLink (Online service) ; Libin, Wang Editorial: Boston : Birkhäuser Boston Fecha de publicación: 2009 Colección: Progress in Nonlinear Differential Equations and Their Applications num. 76 Número de páginas: X, 252 p Il.: online resource ISBN/ISSN/DL: 978-0-8176-4635-6 Idioma : Inglés (eng) Palabras clave: Physics Mathematical analysis Analysis (Mathematics) Differential equations Partial differential Applied mathematics Engineering Elementary particles (Physics) Quantum field theory Particles, Field Theory Theoretical, and Computational Equations Ordinary Applications of Mathematics Clasificación: 51 Matemáticas Resumen: This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically, beginning with introductory material which leads to the original research of the authors. Using the concept of weak linear degeneracy and the method of (generalized) normalized coordinates, this book establishes a systematic theory for the global existence and blowup mechanism of regular nonlinear hyperbolic waves with small amplitude for the Cauchy problem, the Cauchy problem on a semi-bounded initial data, the one-sided mixed initial-boundary value problem, the generalized Riemann problem, the generalized nonlinear initial-boun dary Riemann problem, and some related inverse problems. Motivation is given via a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Global Propagation of Regular Nonlinear Hyperbolic Waves will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves Nota de contenido: Preliminaries -- The Cauchy Problem -- The Cauchy Problem (Continued) -- Cauchy Problem on a Semibounded Initial Axis -- One-Sided Mixed Initial-Boundary Value Problem -- Generalized Riemann Problem -- Generalized Nonlinear Initial-Boundary Riemann Problem -- Inverse Generalized Riemann Problem -- Inverse Piston Problem En línea: http://dx.doi.org/10.1007/b78335 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33935 Global Propagation of Regular Nonlinear Hyperbolic Waves [documento electrónico] / Tatsien, Li ; SpringerLink (Online service) ; Libin, Wang . - Boston : Birkhäuser Boston, 2009 . - X, 252 p : online resource. - (Progress in Nonlinear Differential Equations and Their Applications; 76) .
ISBN : 978-0-8176-4635-6
Idioma : Inglés (eng)
Palabras clave: Physics Mathematical analysis Analysis (Mathematics) Differential equations Partial differential Applied mathematics Engineering Elementary particles (Physics) Quantum field theory Particles, Field Theory Theoretical, and Computational Equations Ordinary Applications of Mathematics Clasificación: 51 Matemáticas Resumen: This monograph describes global propagation of regular nonlinear hyperbolic waves described by first-order quasilinear hyperbolic systems in one dimension. The exposition is clear, concise, and unfolds systematically, beginning with introductory material which leads to the original research of the authors. Using the concept of weak linear degeneracy and the method of (generalized) normalized coordinates, this book establishes a systematic theory for the global existence and blowup mechanism of regular nonlinear hyperbolic waves with small amplitude for the Cauchy problem, the Cauchy problem on a semi-bounded initial data, the one-sided mixed initial-boundary value problem, the generalized Riemann problem, the generalized nonlinear initial-boun dary Riemann problem, and some related inverse problems. Motivation is given via a number of physical examples from the areas of elastic materials, one-dimensional gas dynamics, and waves. Global Propagation of Regular Nonlinear Hyperbolic Waves will stimulate further research and help readers further understand important aspects and recent progress of regular nonlinear hyperbolic waves Nota de contenido: Preliminaries -- The Cauchy Problem -- The Cauchy Problem (Continued) -- Cauchy Problem on a Semibounded Initial Axis -- One-Sided Mixed Initial-Boundary Value Problem -- Generalized Riemann Problem -- Generalized Nonlinear Initial-Boundary Riemann Problem -- Inverse Generalized Riemann Problem -- Inverse Piston Problem En línea: http://dx.doi.org/10.1007/b78335 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33935 Ejemplares
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