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1 Carfora, Mauro Quantum Triangulations I09664 2017 eBook  
2 Platania, Alessia Benedetta Asymptotically Safe Gravity I08869 2018 eBook  
3 Marmo, G Classical and Quantum Physics I08690 2019 eBook  
4 Szabo, Richard J Equivariant Cohomology and Localization of Path Integrals I11316 2000 eBook  
5 Gordon, B. Brent The Arithmetic and Geometry of Algebraic Cycles I10736 2000 eBook  
6 Maeda, Yoshiaki Noncommutative Differential Geometry and Its Applications to Physics I10561 2001 eBook  
7 Bandyopadhyay, P Geometry, Topology and Quantum Field Theory I10559 2003 eBook  
8 Blanchard, Philipp Random Walks and Diffusions on Graphs and Databases I07722 2011 eBook  
9 Schottenloher, Martin A Mathematical Introduction to Conformal Field Theory I07652 2008 eBook  
10 Fursaev, Dmitri Operators, Geometry and Quanta I07445 2011 eBook  
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TitleQuantum Triangulations : Moduli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow
Author(s)Carfora, Mauro;Marzuoli, Annalisa
PublicationCham, 1. Imprint: Springer 2. 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, 1. Imprint: Springer 2. 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, 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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TitleEquivariant Cohomology and Localization of Path Integrals
Author(s)Szabo, Richard J
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. 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, 1. Imprint: Springer 2. 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, 1. Imprint: Springer 2. 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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TitleGeometry, Topology and Quantum Field Theory
Author(s)Bandyopadhyay, P
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2003.
DescriptionXI, 220 p. 1 illus : online resource
Abstract NoteThis is a monograph on geometrical and topological features which arise in quantum field theory. It is well known that when a chiral fermion interacts with a gauge field we have chiral anomaly which corresponds to the fact that divergence of the axial vector current does not vanish. It is observed that this is related to certain topological features associated with the fermion and leads to the realization of the topological origin of fermion number as well as the Berry phase. The role of gauge fields in the quantization procedure has its implications in these topological features of a fermion and helps us to consider a massive fermion as a soliton (skyrrnion). In this formalism chiral anomaly is found to be responsible for mass generation. This has its relevance in electroweak theory where it is observed that weak interaction gauge bosons attain mass topologically. The geometrical feature of a skyrmion also helps us to realize the internal symmetry of hadrons from reflection group. Finally it has been shown that noncommutative geometry where the space time manifold is taken to be X = M x Zz has its relevance in the description of a massive 4 fermion as a skyrmion when the discrete space is considered as the internal space and the symmetry breaking leads to chiral anomaly. In chap. l preliminary mathematical formulations related to the spinor structure have been discussed. In chap
ISBN,Price9789401716970
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. Heavy ions 9. Manifolds (Mathematics) 10. NUCLEAR PHYSICS 11. Nuclear Physics, Heavy Ions, Hadrons 12. QUANTUM FIELD THEORY 13. QUANTUM PHYSICS
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TitleRandom Walks and Diffusions on Graphs and Databases : An Introduction
Author(s)Blanchard, Philipp;Volchenkov, Dimitri
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2011.
DescriptionXIV, 262 p : online resource
Abstract NoteMost networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks
ISBN,Price9783642195921
Keyword(s)1. Applications of Graph Theory and Complex Networks 2. COMPLEX MANIFOLDS 3. COMPLEXITY 4. COMPUTATIONAL COMPLEXITY 5. Data structures (Computer science) 6. Data Structures and Information Theory 7. EBOOK 8. EBOOK - SPRINGER 9. Manifolds (Mathematics) 10. Manifolds and Cell Complexes (incl. Diff.Topology) 11. PHYSICS
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9.     
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TitleA Mathematical Introduction to Conformal Field Theory
Author(s)Schottenloher, Martin
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2008.
DescriptionXV, 249 p : online resource
Abstract NoteThe first part of this book gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. In particular, the conformal groups are determined and the appearance of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. The second part surveys some more advanced topics of conformal field theory, such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface. The substantially revised and enlarged second edition makes in particular the second part of the book more self-contained and tutorial, with many more examples given. Furthermore, two new chapters on Wightman's axioms for quantum field theory and vertex algebras broaden the survey of advanced topics. An outlook making the connection with most recent developments has also been added
ISBN,Price9783540686286
Keyword(s)1. ALGEBRA 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. PHYSICS 11. Quantum Field Theories, String Theory 12. QUANTUM FIELD THEORY 13. STRING THEORY
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10.    
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TitleOperators, Geometry and Quanta : Methods of Spectral Geometry in Quantum Field Theory
Author(s)Fursaev, Dmitri;Vassilevich, Dmitri
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2011.
DescriptionXVI, 288 p : online resource
Abstract NoteThis book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). More than hundred exercises together with their solutions are included.??This book addresses advanced graduate students and researchers in mathematical physics and in neighbouring areas??with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions
ISBN,Price9789400702059
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GLOBAL ANALYSIS (MATHEMATICS) 4. Global Analysis and Analysis on Manifolds 5. Manifolds (Mathematics) 6. Mathematical Methods in Physics 7. PHYSICS 8. Quantum Field Theories, String Theory 9. QUANTUM FIELD THEORY 10. STRING THEORY
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