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1 Khakshournia, Samad The Art of Gluing Space-Time Manifolds I12922 2023 eBook  
2 Cecotti, Sergio Introduction to String Theory I12853 2023 eBook  
3 Bargue??o, Pedro The Geroch-Held-Penrose Calculus I12839 2023 eBook  
4 Nielsen, Frank Progress in Information Geometry I11629 2021 eBook  
5 Carfora, Mauro Quantum Triangulations I09664 2017 eBook  
6 Platania, Alessia Benedetta Asymptotically Safe Gravity I08869 2018 eBook  
7 Marmo, G Classical and Quantum Physics I08690 2019 eBook  
8 Szabo, Richard J Equivariant Cohomology and Localization of Path Integrals I11316 2000 eBook  
9 Gordon, B. Brent The Arithmetic and Geometry of Algebraic Cycles I10736 2000 eBook  
10 Maeda, Yoshiaki Noncommutative Differential Geometry and Its Applications to Physics I10561 2001 eBook  
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TitleThe Art of Gluing Space-Time Manifolds : Methods and Applications
Author(s)Khakshournia, Samad;Mansouri, Reza
PublicationCham, 1. Imprint: Springer 2. Springer Nature Switzerland, 2023.
DescriptionVIII, 122 p. 1 illus : online resource
Abstract NoteThis concise book reviews methods used for gluing space-time manifolds together. It is therefore relevant to theorists working on branes, walls, domain walls, concepts frequently used in theoretical cosmology, astrophysics, and gravity theory. Nowadays, applications are also in theoretical condensed matter physics where Riemannian geometry appears. The book also reviews the history of matching conditions between two space-time manifolds from the early times of general relativity up to now
ISBN,Price9783031486128
Keyword(s)1. Classical and Quantum Gravity 2. CONDENSED MATTER 3. CONDENSED MATTER PHYSICS 4. COSMOLOGY 5. DIFFERENTIAL GEOMETRY 6. EBOOK - SPRINGER 7. GENERAL RELATIVITY 8. GENERAL RELATIVITY (PHYSICS) 9. GEOMETRY, DIFFERENTIAL 10. GLOBAL ANALYSIS (MATHEMATICS) 11. Global Analysis and Analysis on Manifolds 12. GRAVITATION 13. Manifolds (Mathematics)
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TitleIntroduction to String Theory
Author(s)Cecotti, Sergio
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2023.
DescriptionXXIX, 828 p. 30 illus : online resource
Abstract NoteGraduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book???s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader???s understanding of the underlying math. In writing this book,the author???s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts.
ISBN,Price9783031365300
Keyword(s)1. Classical and Quantum Gravity 2. EBOOK - SPRINGER 3. GRAVITATION 4. Manifolds (Mathematics) 5. Manifolds and Cell Complexes 6. MATHEMATICAL PHYSICS 7. PARTICLE PHYSICS 8. PARTICLES (NUCLEAR PHYSICS) 9. Theoretical, Mathematical and Computational Physics
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TitleThe Geroch-Held-Penrose Calculus : Fundamentals and Applications
Author(s)Bargue??o, Pedro;Contreras, Ernesto
PublicationCham, 1. Imprint: Springer 2. Springer Nature Switzerland, 2023.
DescriptionXVI, 70 p. 2 illus : online resource
Abstract NoteThis book offers a primer on the fundamentals and applications of the Geroch-Held-Penrose (GHP) calculus, a powerful formalism designed for spacetimes that occur frequently in the teaching of General Relativity. Specifically, the book shows in detail the power of the calculus when dealing with spherically symmetric spacetimes. After introducing the basics, a new look at all the classical spherically symmetric black hole solutions is given within the GHP formalism. This is then employed to give new insights into the Tolman-Oppenheimer-Volkoff equations for stellar structure, including a derivation of new exact anisotropic fluid solutions. Finally, a re-writing of some essential features of black hole thermodynamics within the GHP formalism is performed. The book is based on the authors' lecture notes, used in their undergraduate and graduate lectures and while supervising their upper undergraduate and graduate students. To fully benefit from this concise primer, readers only need an undergraduate background in general relativity
ISBN,Price9783031429484
Keyword(s)1. EBOOK - SPRINGER 2. Foundations of Physics and Cosmology 3. GENERAL RELATIVITY 4. GENERAL RELATIVITY (PHYSICS) 5. GLOBAL ANALYSIS (MATHEMATICS) 6. Global Analysis and Analysis on Manifolds 7. Integral Transforms and Operational Calculus 8. Manifolds (Mathematics) 9. MATHEMATICAL ANALYSIS 10. MATHEMATICAL PHYSICS 11. SCIENCE 12. Theoretical, Mathematical and Computational Physics
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TitleProgress in Information Geometry : Theory and Applications
Author(s)Nielsen, Frank
PublicationCham, Springer International Publishing, 2021.
DescriptionXII, 274 p. 105 illus., 35 illus. in color : online resource
Abstract NoteThis book focuses on information-geometric manifolds of structured data and models and related applied mathematics. It features new and fruitful interactions between several branches of science: Advanced Signal/Image/Video Processing, Complex Data Modeling and Analysis, Statistics on Manifolds, Topology/Machine/Deep Learning and Artificial Intelligence. The selection of applications makes the book a substantial information source, not only for academic scientist but it is also highly relevant for industry. The book project was initiated following discussions at the international conference GSI???2019 ??? Geometric Science of Information that was held at ENAC, Toulouse (France)
ISBN,Price9783030654597
Keyword(s)1. Coding and Information Theory 2. CODING THEORY 3. Communications Engineering, Networks 4. COMPLEX SYSTEMS 5. EBOOK 6. EBOOK - SPRINGER 7. GLOBAL ANALYSIS (MATHEMATICS) 8. Global Analysis and Analysis on Manifolds 9. INFORMATION THEORY 10. Manifolds (Mathematics) 11. SIGNAL PROCESSING 12. Signal, Speech and Image Processing 13. Statistics in Engineering, Physics, Computer Science, Chemistry and Earth Sciences 14. Statistics?? 15. SYSTEM THEORY 16. TELECOMMUNICATION
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TitleQuantum Triangulations : Moduli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow
Author(s)Carfora, Mauro;Marzuoli, Annalisa
PublicationCham, Springer International Publishing, 2017.
DescriptionXX, 392 p. 113 illus., 92 illus. in color : online resource
Abstract NoteThis book discusses key conceptual aspects and explores the connection between triangulated manifolds and quantum physics, using a set of case studies ranging from moduli space theory to quantum computing to provide an accessible introduction to this topic. Research on polyhedral manifolds often reveals unexpected connections between very distinct aspects of mathematics and physics. In particular, triangulated manifolds play an important role in settings such as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, critical phenomena and complex systems. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is also often a consequence of an underlying structure that naturally calls into play non-trivial aspects of representation theory, complex analysis and topology in a way that makes the basic geometric structures of the physical interactions involved clear. This second edition further emphasizes the essential role that triangulations play in modern mathematical physics, with a new and highly detailed chapter on the geometry of the dilatonic non-linear sigma model and its subtle and many-faceted connection with Ricci flow theory. This connection is treated in depth, pinpointing both the mathematical and physical aspects of the perturbative embedding of the Ricci flow in the renormalization group flow of non-linear sigma models. The geometry of the dilaton field is discussed from a novel standpoint by using polyhedral manifolds and Riemannian metric measure spaces, emphasizing their role in connecting non-linear sigma models??? effective action to Perelman???s energy-functional. No other published account of this matter is so detailed and informative. This new edition also features an expanded appendix on Riemannian geometry, and a rich set of new illustrations to help the reader grasp the more difficult points of the theory. The book offers a valuable guide for all mathematicians and theoretical physicists working in the field of quantum geometry and its ??applications
ISBN,Price9783319679372
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. COMPLEX MANIFOLDS 3. EBOOK 4. EBOOK - SPRINGER 5. GRAVITATION 6. Manifolds (Mathematics) 7. Manifolds and Cell Complexes (incl. Diff.Topology) 8. Mathematical Applications in the Physical Sciences 9. MATHEMATICAL PHYSICS 10. Numerical and Computational Physics, Simulation 11. PHYSICS 12. QUANTUM PHYSICS
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TitleAsymptotically Safe Gravity : From Spacetime Foliation to Cosmology
Author(s)Platania, Alessia Benedetta
PublicationCham, Springer International Publishing, 2018.
DescriptionXV, 142 p. 87 illus., 13 illus. in color : online resource
Abstract NoteThis book seeks to construct a consistent fundamental quantum theory of gravity, which is often considered one of the most challenging open problems in present-day physics. It approaches this challenge using modern functional renormalization group techniques, and attempts to realize the idea of ???Asymptotic Safety??? originally proposed by S. Weinberg. Quite remarkably, the book makes significant progress regarding both the fundamental aspects of the program and its phenomenological consequences. The conceptual developments pioneer the construction of a well-behaved functional renormalization group equation adapted to spacetimes with a preferred time-direction. It is demonstrated that the Asymptotic Safety mechanism persists in this setting and extends to many phenomenologically interesting gravity-matter systems. These achievements constitute groundbreaking steps towards bridging the gap between quantum gravity in Euclidean and Lorentzian spacetimes. The phenomenological applications cover core topics in quantum gravity, e.g. constructing a phenomenologically viable cosmological evolution based on quantum gravity effects in the very early universe, and analyzing quantum corrections to black holes forming from a spherical collapse. As a key feature, all developments are presented in a comprehensive and accessible way. This makes the work a timely and valuable guide into the rapidly evolving field of Asymptotic Safety
ISBN,Price9783319987941
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. COMPLEX MANIFOLDS 3. COSMOLOGY 4. EBOOK 5. EBOOK - SPRINGER 6. GRAVITATION 7. Manifolds (Mathematics) 8. Manifolds and Cell Complexes (incl. Diff.Topology)
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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, 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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TitleEquivariant Cohomology and Localization of Path Integrals
Author(s)Szabo, Richard J
PublicationBerlin, Heidelberg, Springer Berlin Heidelberg, 2000.
DescriptionXI, 315 p : online resource
Abstract NoteThis book, addressing both researchers and graduate students, reviews equivariant localization techniques for the evaluation of Feynman path integrals. The author gives the relevant mathematical background in some detail, showing at the same time how localization ideas are related to classical integrability. The text explores the symmetries inherent in localizable models for assessing the applicability of localization formulae. Various applications from physics and mathematics are presented
ISBN,Price9783540465508
Keyword(s)1. ALGEBRAIC TOPOLOGY 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. GLOBAL ANALYSIS (MATHEMATICS) 7. Global Analysis and Analysis on Manifolds 8. Manifolds (Mathematics) 9. Mathematical Methods in Physics 10. NUCLEAR PHYSICS 11. Particle and Nuclear Physics 12. PHYSICS 13. QUANTUM FIELD THEORY 14. TOPOLOGY
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TitleThe Arithmetic and Geometry of Algebraic Cycles
Author(s)Gordon, B. Brent;Lewis, James D;M??ller-Stach, Stefan;Saito, Shuji;Yui, Noriko
PublicationDordrecht, Springer Netherlands, 2000.
DescriptionXXX, 615 p : online resource
Abstract NoteThe NATO Advanced Study Institute on "The Arithmetic and Geometry of Algebraic Cycles" was held at the Banff Centre for Conferences in Banff (Al?? berta, Canada) from June 7 until June 19, 1998. This meeting was organized jointly with Centre de Recherches Mathematiques (CRM), Montreal, as one of the CRM Summer schools which take place annually at the Banff Center. The conference also served as the kick-off activity of the CRM 1998-99 theme year on Number Theory and Arithmetic Geometry. There were 109 participants who came from 17 countries: Belgium, Canada, China, France, Germany, Greece, India, Italy, Japan, Mexico, Netherlands, - mania, Russia, Spain, Switzerland, the United Kingdom and the United States. During a period of two weeks, 41 invited lectures and 20 contributed lec?? tures were presented. Four lectures by invited speakers were delivered every day, followed by two sessions of contributed talks. Many informal discussions and working sessions involving small groups were organized by individual partic?? ipants. In addition, participants' reprints and preprints were displayed through?? out in a lounge next to the auditorium, which further enhanced opportunities for communication and interaction
ISBN,Price9789401140980
Keyword(s)1. ALGEBRA 2. ALGEBRAIC GEOMETRY 3. Applications of Mathematics 4. APPLIED MATHEMATICS 5. EBOOK 6. EBOOK - SPRINGER 7. ENGINEERING MATHEMATICS 8. Field theory (Physics) 9. Field Theory and Polynomials 10. GLOBAL ANALYSIS (MATHEMATICS) 11. Global Analysis and Analysis on Manifolds 12. K-THEORY 13. Manifolds (Mathematics)
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TitleNoncommutative Differential Geometry and Its Applications to Physics : Proceedings of the Workshop at Shonan, Japan, June 1999
Author(s)Maeda, Yoshiaki;Moriyoshi, Hitoshi;Omori, Hideki;Sternheimer, Daniel;Tate, Tatsuya;Watamura, Satoshi
PublicationDordrecht, Springer Netherlands, 2001.
DescriptionVIII, 308 p : online resource
Abstract NoteNoncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics
ISBN,Price9789401007047
Keyword(s)1. DIFFERENTIAL GEOMETRY 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. GLOBAL ANALYSIS (MATHEMATICS) 7. Global Analysis and Analysis on Manifolds 8. INTEGRAL TRANSFORMS 9. Integral Transforms, Operational Calculus 10. Manifolds (Mathematics) 11. Operational calculus 12. QUANTUM FIELD THEORY 13. QUANTUM PHYSICS
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