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1 Tristan Needham Visual differential geometry and forms: A Mathematical Drama in Five Acts 026961 2021 Book  
2 Rodrigues, Jr, Waldyr A The Many Faces of Maxwell, Dirac and Einstein Equations I10404 2016 eBook  
3 Fr??, Pietro Giuseppe Advances in Geometry and Lie Algebras from Supergravity I10019 2018 eBook  
4 Rowe, David E Beyond Einstein I09813 2018 eBook  
5 Rudolph, Gerd Differential Geometry and Mathematical Physics I09737 2017 eBook  
6 Lehmkuhl, Dennis Towards a Theory of Spacetime Theories I09130 2017 eBook  
7 De Bianchi, Silvia One Hundred Years of Gauge Theory I09028 2020 eBook  
8 Boskoff, Wladimir-Georges A Mathematical Journey to Relativity I08812 2020 eBook  
9 Marmo, G Classical and Quantum Physics I08690 2019 eBook  
10 Schmidt, Bernd G Einstein???s Field Equations and Their Physical Implications I11510 2000 eBook  
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TitleVisual differential geometry and forms: A Mathematical Drama in Five Acts
Author(s)Tristan Needham
PublicationUSA, Princeton University Press, 2021.
DescriptionPB : 584pp
Abstract NoteAn inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner.Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book.Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
ISBN,Price978-0691203706 : $ 45.00
Classification1. 514.7 NEE 2. 514.77 NEE 3. 517.7 NEE
Keyword(s)1. DIFFERENTIAL GEOMETRY 2. Forms 3. Geometry and Forms
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026961     Issued UV01: Vishal Upendran 24/Aug/2022

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TitleThe Many Faces of Maxwell, Dirac and Einstein Equations : A Clifford Bundle Approach
Author(s)Rodrigues, Jr, Waldyr A;Capelas de Oliveira, Edmundo
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2016.
DescriptionXVI, 587 p. 14 illus : online resource
Abstract NoteThis book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research. This thoroughly revised second edition also adds three new chapters: on the Clifford bundle approach to the Riemannian or semi-Riemannian differential geometry of branes; on Komar currents in the context of the General Relativity theory; and an analysis of the similarities and main differences between Dirac, Majorana and ELKO spinor fields. The exercises with solutions, the comprehensive list of mathematical symbols, and the list of acronyms and abbreviations are provided for self-study for students as well as for classes. From the reviews of the first edition: ???The text is written in a very readable manner and is complemented with plenty of worked-out exercises which are in the style of extended examples. ... their book could also serve as a textbook for graduate students in physics or mathematics." (Alberto Molgado, Mathematical Reviews, 2008 k)
ISBN,Price9783319276373
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. GRAVITATION 6. Mathematical Applications in the Physical Sciences 7. MATHEMATICAL PHYSICS
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TitleAdvances in Geometry and Lie Algebras from Supergravity
Author(s)Fr??, Pietro Giuseppe
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2018.
DescriptionXX, 556 p. 64 illus., 32 illus. in color : online resource
Abstract NoteThis book aims to provide an overview of several topics in advanced Differential Geometry and Lie Group Theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject.??
ISBN,Price9783319744919
Keyword(s)1. DIFFERENTIAL GEOMETRY 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. History and Philosophical Foundations of Physics 7. MATHEMATICAL PHYSICS 8. PHYSICS 9. QUANTUM FIELD THEORY 10. Theoretical, Mathematical and Computational Physics
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TitleBeyond Einstein : Perspectives on Geometry, Gravitation, and Cosmology in the Twentieth Century
Author(s)Rowe, David E;Sauer, Tilman;Walter, Scott A
PublicationNew York, NY, 1. Imprint: Birkh??user 2. Springer New York, 2018.
DescriptionXXIII, 492 p. 71 illus., 14 illus. in color : online resource
Abstract NoteThis volume explores the interplay between mathematical and physical research and the interactions of twentieth-century scientists within their academic communities. Beginning with Einstein???s general theory of relativity, the authors investigate a series of dramatic discoveries and rival theories in physics that influenced the development of modern differential geometry. Other sections recount the numerous methods, like the resurgence of Weyl geometry, used by geometers to solve the problems revealed by those same innovations in space-time physics. The effect of general relativity on astronomy is also addressed, namely how astronomers worked through new theories like inflationary cosmology and Phoenix models. By including recent historical research and coupling this work with many disciplines??? unique perspectives, this text provides a rich picture of general relativity and cosmology over the course of the twentieth century. The increased study on the documentation of Einstein???s early scientific work has clarified the history of science for that time and profoundly altered the way scientists view their own work, as this interdisciplinary volume demonstrates
ISBN,Price9781493977086
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. GRAVITATION 6. HISTORY 7. History of Mathematical Sciences 8. MATHEMATICS 9. Philosophy and science 10. PHILOSOPHY OF SCIENCE 11. QUANTUM PHYSICS
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TitleDifferential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields
Author(s)Rudolph, Gerd;Schmidt, Matthias
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2017.
DescriptionXVI, 830 p. 15 illus., 2 illus. in color : online resource
Abstract NoteThe book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks: - Geometry and topology of fibre bundles, - Clifford algebras, spin structures and Dirac operators, - Gauge theory. Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory. The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces. Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the non-generic gauge orbit strata in the framework of Hamiltonian lattice gauge theory. The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level
ISBN,Price9789402409598
Keyword(s)1. ALGEBRAIC GEOMETRY 2. ALGEBRAIC TOPOLOGY 3. DIFFERENTIAL GEOMETRY 4. EBOOK 5. EBOOK - SPRINGER 6. Elementary particles (Physics) 7. Elementary Particles, Quantum Field Theory 8. Mathematical Methods in Physics 9. MATHEMATICAL PHYSICS 10. PHYSICS 11. QUANTUM FIELD THEORY
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TitleTowards a Theory of Spacetime Theories
Author(s)Lehmkuhl, Dennis;Schiemann, Gregor;Scholz, Erhard
PublicationNew York, NY, 1. Imprint: Birkh??user 2. Springer New York, 2017.
DescriptionVIII, 335 p. 7 illus : online resource
Abstract NoteThis contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the ???best??? theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the ???space of spacetime theories.??? This work will be of interest to physicists, as well as philosophers and historians of science working with or interested in General Relativity and/or Space, Time and Gravitation more generally
ISBN,Price9781493932108
Keyword(s)1. DIFFERENTIAL GEOMETRY 2. EBOOK 3. EBOOK - SPRINGER 4. HISTORY 5. History of Mathematical Sciences 6. MATHEMATICAL PHYSICS 7. MATHEMATICS 8. Theoretical, Mathematical and Computational Physics
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TitleOne Hundred Years of Gauge Theory : Past, Present and Future Perspectives
Author(s)De Bianchi, Silvia;Kiefer, Claus
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2020.
DescriptionXII, 313 p. 28 illus., 12 illus. in color : online resource
Abstract NoteThis book presents a multidisciplinary guide to gauge theory and gravity, with chapters by the world???s leading theoretical physicists, mathematicians, historians and philosophers of science. The contributions from theoretical physics explore e.g. the consistency of the unification of gravitation and quantum theory, the underpinnings of experimental tests of gauge theory and its role in shedding light on the relationship between mathematics and physics. In turn, historians and philosophers of science assess the impact of Weyl???s view on the philosophy of science. Graduate students, lecturers and researchers in the fields of history of science, theoretical physics and philosophy of science will benefit from this book by learning about the role played by Weyl???s Raum-Zeit-Materie in shaping several modern research fields, and by gaining insights into the future prospects of gauge theory in both theoretical and experimental physics. Furthermore, the book facilitates interdisciplinary exchange and conceptual innovation in tackling fundamental questions about our deepest theories of physics. Chapter ???Weyl???s Raum-Zeit-Materie and the Philosophy of Science??? is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com
ISBN,Price9783030511975
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. Elementary particles (Physics) 6. Elementary Particles, Quantum Field Theory 7. GRAVITATION 8. History and Philosophical Foundations of Physics 9. Philosophy and science 10. PHILOSOPHY OF SCIENCE 11. PHYSICS 12. QUANTUM FIELD THEORY
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TitleA Mathematical Journey to Relativity : Deriving Special and General Relativity with Basic Mathematics
Author(s)Boskoff, Wladimir-Georges;Capozziello, Salvatore
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2020.
DescriptionXXII, 397 p. 44 illus., 6 illus. in color : online resource
Abstract NoteThis book opens with an axiomatic description of Euclidean and non-Euclidean geometries. Euclidean geometry is the starting point to understand all other geometries and it is the cornerstone for our basic intuition of vector spaces. The generalization to non-Euclidean geometry is the following step to develop the language of Special and General Relativity. These theories are discussed starting from a full geometric point of view. Differential geometry is presented in the simplest way and it is applied to describe the physical world. The final result of this construction is deriving the Einstein field equations for gravitation and spacetime dynamics. Possible solutions, and their physical implications are also discussed: the Schwarzschild metric, the relativistic trajectory of planets, the deflection of light, the black holes, the cosmological solutions like de Sitter, Friedmann-Lema??tre-Robertson-Walker, and G??del ones. Some current problems like dark energy are also scketched. The book is self-contained and includes details of all proofs. It provides solutions or tips to solve problems and exercises. It is designed for undergraduate students and for all readers who want a first geometric approach to Special and General Relativity
ISBN,Price9783030478940
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. GRAVITATION 6. Mathematical Methods in Physics 7. MATHEMATICAL PHYSICS 8. PHYSICS 9. QUANTUM PHYSICS 10. Theoretical, Mathematical and Computational Physics
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TitleClassical and Quantum Physics : 60 Years Alberto Ibort Fest Geometry, Dynamics, and Control
Author(s)Marmo, G;Mart??n de Diego, David;Mu??oz Lecanda, Miguel
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2019.
DescriptionXXVI, 374 p. 46 illus., 14 illus. in color : online resource
Abstract NoteThis proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas. Most of Albertos???s scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics. Let us mention some of the fields of expertise of Alberto Ibort: Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others. In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic. His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed
ISBN,Price9783030247485
Keyword(s)1. Associative rings 2. Associative Rings and Algebras 3. CALCULUS OF VARIATIONS 4. Calculus of Variations and Optimal Control; Optimization 5. COMPLEX MANIFOLDS 6. DIFFERENTIAL GEOMETRY 7. EBOOK 8. EBOOK - SPRINGER 9. Manifolds (Mathematics) 10. Manifolds and Cell Complexes (incl. Diff.Topology) 11. MATHEMATICAL PHYSICS 12. Rings (Algebra) 13. Theoretical, Mathematical and Computational Physics
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TitleEinstein???s Field Equations and Their Physical Implications : Selected Essays in Honour of J??rgen Ehlers
Author(s)Schmidt, Bernd G
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2000.
DescriptionXIII, 433 p : online resource
Abstract NoteThis book serves two purposes. The authors present important aspects of modern research on the mathematical structure of Einstein's field equations and they show how to extract their physical content from them by mathematically exact methods. The essays are devoted to exact solutions and to the Cauchy problem of the field equations as well as to post-Newtonian approximations that have direct physical implications. Further topics concern quantum gravity and optics in gravitational fields. The book addresses researchers in relativity and differential geometry but can also be used as additional reading material for graduate students.
ISBN,Price9783540465805
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. GRAVITATION 6. Mathematical Methods in Physics 7. PHYSICS
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I11510     On Shelf    

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