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1 Szabo, Richard J Equivariant Cohomology and Localization of Path Integrals I11316 2000 eBook  
2 Gordon, B. Brent The Arithmetic and Geometry of Algebraic Cycles I10736 2000 eBook  
3 Maeda, Yoshiaki Noncommutative Differential Geometry and Its Applications to Physics I10561 2001 eBook  
4 Bandyopadhyay, P Geometry, Topology and Quantum Field Theory I10559 2003 eBook  
5 Schottenloher, Martin A Mathematical Introduction to Conformal Field Theory I07652 2008 eBook  
6 Fursaev, Dmitri Operators, Geometry and Quanta I07445 2011 eBook  
7 Gliklikh, Yuri E Global and Stochastic Analysis with Applications to Mathematical Physics I06899 2011 eBook  
8 Rudolph, Gerd Differential Geometry and Mathematical Physics I06330 2013 eBook  
9 Das, Anadijiban The General Theory of Relativity I05717 2012 eBook  
10 Schroeck Jr., Franklin E Quantum Mechanics on Phase Space I04439 1996 eBook  
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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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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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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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TitleGlobal and Stochastic Analysis with Applications to Mathematical Physics
Author(s)Gliklikh, Yuri E
PublicationLondon, 1. Imprint: Springer 2. Springer London, 2011.
DescriptionXXIV, 436 p : online resource
Abstract NoteMethods of global analysis and stochastic analysis are most often applied in mathematical physics as separate entities, thus forming important directions in the field. However, while combination of the two subject areas is rare, it is fundamental for the consideration of a broader class of problems This book develops methods of Global Analysis and Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as divergent and requiring different methods of investigation Global and Stochastic Analysis with Applications to Mathematical Physics covers branches of mathematics that are currently absent in monograph form. Through the demonstration of new topics of investigation and results, both in traditional and more recent problems, this book offers a fresh perspective on ordinary and stochastic differential equations and inclusions (in particular, given in terms of Nelson's mean derivatives) on linear spaces and manifolds. Topics covered include classical mechanics on non-linear configuration spaces, problems of statistical and quantum physics, and hydrodynamics A self-contained book that provides a large amount of preliminary material and recent results which will serve to be a useful introduction to the subject and a valuable resource for further research. It will appeal to researchers, graduate and PhD students working in global analysis, stochastic analysis and mathematical physics
ISBN,Price9780857291639
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. PROBABILITIES 9. Probability Theory and Stochastic Processes
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8.     
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TitleDifferential Geometry and Mathematical Physics : Part I. Manifolds, Lie Groups and Hamiltonian Systems
Author(s)Rudolph, Gerd;Schmidt, Matthias
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 2013.
DescriptionXIV, 762 p : online resource
Abstract NoteStarting from an undergraduate level, this book systematically develops the basics of ??? Calculus on manifolds, vector bundles, vector fields and differential forms, ??? Lie groups and Lie group actions, ??? Linear symplectic algebra and symplectic geometry, ??? Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact
ISBN,Price9789400753457
Keyword(s)1. CLASSICAL MECHANICS 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. GLOBAL ANALYSIS (MATHEMATICS) 6. Global Analysis and Analysis on Manifolds 7. LIE GROUPS 8. Manifolds (Mathematics) 9. Mathematical Methods in Physics 10. MECHANICS 11. PHYSICS 12. TOPOLOGICAL GROUPS 13. Topological Groups, Lie Groups
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9.     
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TitleThe General Theory of Relativity : A Mathematical Exposition
Author(s)Das, Anadijiban;DeBenedictis, Andrew
PublicationNew York, NY, 1. Imprint: Springer 2. Springer New York, 2012.
DescriptionXXVI, 678 p : online resource
Abstract Note??The General Theory of Relativity: A Mathematical Exposition will serve readers as a modern mathematical introduction to the general theory of relativity. Throughout the book, examples, worked-out problems, and exercises (with hints and solutions) are furnished. Topics in this book include, but are not limited to: ??? tensor analysis ??? the special theory of relativity ??? the general theory of relativity and Einstein???s field equations ??? spherically symmetric solutions and experimental confirmations ??? static and stationary space-time domains ??? black holes ??? cosmological models ??? algebraic classifications and the Newman-Penrose equations ??? the coupled Einstein-Maxwell-Klein-Gordon equations ??? appendices covering mathematical supplements and special topics Mathematical rigor, yet very clear presentation of the topics make this book a unique text for both university students and research scholars. Anadijiban Das has taught courses on Relativity Theory at The University College of Dublin, Ireland; Jadavpur University, India; Carnegie-Mellon University, USA; and Simon Fraser University, Canada. His major areas of research include, among diverse topics, the mathematical aspects of general relativity theory. Andrew DeBenedictis has taught courses in Theoretical Physics at Simon Fraser University, Canada, and is also a member of The Pacific Institute for the Mathematical Sciences. His research interests include quantum gravity, classical gravity, and semi-classical gravity
ISBN,Price9781461436584
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. COSMOLOGY 3. EBOOK 4. EBOOK - SPRINGER 5. GLOBAL ANALYSIS (MATHEMATICS) 6. Global Analysis and Analysis on Manifolds 7. GRAVITATION 8. Manifolds (Mathematics) 9. Mathematical Applications in the Physical Sciences 10. MATHEMATICAL PHYSICS
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10.    
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TitleQuantum Mechanics on Phase Space
Author(s)Schroeck Jr., Franklin E
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1996.
DescriptionXVI, 672 p : online resource
Abstract NoteIn this monograph, we shall present a new mathematical formulation of quantum theory, clarify a number of discrepancies within the prior formulation of quantum theory, give new applications to experiments in physics, and extend the realm of application of quantum theory well beyond physics. Here, we motivate this new formulation and sketch how it developed. Since the publication of Dirac's famous book on quantum mechanics [Dirac, 1930] and von Neumann's classic text on the mathematical foundations of quantum mechanics two years later [von Neumann, 1932], there have appeared a number of lines of development, the intent of each being to enrich quantum theory by extra?? polating or even modifying the original basic structure. These lines of development have seemed to go in different directions, the major directions of which are identified here: First is the introduction of group theoretical methods [Weyl, 1928; Wigner, 1931] with the natural extension to coherent state theory [Klauder and Sudarshan, 1968; Peremolov, 1971]. The call for an axiomatic approach to physics [Hilbert, 1900; Sixth Problem] led to the development of quantum logic [Mackey, 1963; Jauch, 1968; Varadarajan, 1968, 1970; Piron, 1976; Beltrametti & Cassinelli, 1981], to the creation of the operational approach [Ludwig, 1983-85, 1985; Davies, 1976] with its application to quantum communication theory [Helstrom, 1976; Holevo, 1982), and to the development of the C* approach [Emch, 1972]. An approach through stochastic differential equations ("stochastic mechanics") was developed [Nelson, 1964, 1966, 1967]
ISBN,Price9789401728300
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GLOBAL ANALYSIS (MATHEMATICS) 4. Global Analysis and Analysis on Manifolds 5. Imaging / Radiology 6. LIE GROUPS 7. Manifolds (Mathematics) 8. Neurosciences 9. QUANTUM PHYSICS 10. Radiology 11. Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences 12. Statistics?? 13. TOPOLOGICAL GROUPS 14. Topological Groups, Lie Groups
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