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1 Patrascu, Andrei-Tudor The Universal Coefficient Theorem and Quantum Field Theory I09785 2017 eBook  
2 Rudolph, Gerd Differential Geometry and Mathematical Physics I09737 2017 eBook  
3 Tanaka, Hiro Lee Lectures on Factorization Homology, ???-Categories, and Topological Field Theories I09620 2020 eBook  
4 Szabo, Richard J Equivariant Cohomology and Localization of Path Integrals I11316 2000 eBook  
5 Carow-Watamura, Ursula Quantum Field Theory and Noncommutative Geometry I08223 2005 eBook  
6 Alabiso, Carlo A Primer on Hilbert Space Theory I08208 2015 eBook  
7 Schlichenmaier, Martin An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces I07756 2007 eBook  
8 Jardine, John F Algebraic K-Theory: Connections with Geometry and Topology I03578 1989 eBook  
9 Goerss, P.G Algebraic K-Theory and Algebraic Topology I02299 1993 eBook  
10 Schlichenmaier, Martin An Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces I02274 1989 eBook  
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TitleThe Universal Coefficient Theorem and Quantum Field Theory : A Topological Guide for the Duality Seeker
Author(s)Patrascu, Andrei-Tudor
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXVI, 270 p. 6 illus., 1 illus. in color : online resource
Abstract NoteThis thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics???one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics
ISBN,Price9783319461434
Keyword(s)1. ALGEBRAIC TOPOLOGY 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. Mathematical Applications in the Physical Sciences 7. MATHEMATICAL PHYSICS 8. Quantum Field Theories, String Theory 9. QUANTUM FIELD THEORY 10. STRING THEORY
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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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TitleLectures on Factorization Homology, ???-Categories, and Topological Field Theories
Author(s)Tanaka, Hiro Lee
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2020.
DescriptionXII, 84 p. 13 illus., 2 illus. in color : online resource
Abstract NoteThis book provides an informal and geodesic introduction to factorization homology, focusing on providing intuition through simple examples. Along the way, the reader is also introduced to modern ideas in homotopy theory and category theory, particularly as it relates to the use of infinity-categories. As with the original lectures, the text is meant to be a leisurely read suitable for advanced graduate students and interested researchers in topology and adjacent fields
ISBN,Price9783030611637
Keyword(s)1. ALGEBRAIC TOPOLOGY 2. Category theory (Mathematics) 3. Category Theory, Homological Algebra 4. EBOOK 5. EBOOK - SPRINGER 6. Homological algebra 7. MATHEMATICAL PHYSICS 8. 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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TitleQuantum Field Theory and Noncommutative Geometry
Author(s)Carow-Watamura, Ursula;Maeda, Yoshiaki;Watamura, Satoshi
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2005.
DescriptionX, 298 p : online resource
Abstract NoteThis volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challenge is posed by gravity, which probably necessitates extension of these methods to geometries with minimum length and therefore quantization of space. This volume builds on the lectures and talks that have been given at a recent meeting on "Quantum Field Theory and Noncommutative Geometry." A considerable effort has been invested in making the contributions accessible to a wider community of readers - so this volume will not only benefit researchers in the field but also postgraduate students and scientists from related areas wishing to become better acquainted with this field
ISBN,Price9783540315261
Keyword(s)1. ALGEBRAIC TOPOLOGY 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. Elementary particles (Physics) 6. Elementary Particles, Quantum Field Theory 7. LIE GROUPS 8. Mathematical Methods in Physics 9. PHYSICS 10. QUANTUM FIELD THEORY 11. TOPOLOGICAL GROUPS 12. Topological Groups, Lie Groups
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I08223     On Shelf    

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TitleA Primer on Hilbert Space Theory : Linear Spaces, Topological Spaces, Metric Spaces, Normed Spaces, and Topological Groups
Author(s)Alabiso, Carlo;Weiss, Ittay
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2015.
DescriptionXVII, 255 p. 5 illus : online resource
Abstract NoteThis book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all subjects has been enriched. Moreover, a brief introduction to topological groups has been added in addition to exercises and solved problems throughout the text. With these improvements, the book can be used in upper undergraduate and lower graduate courses, both in Physics and in Mathematics
ISBN,Price9783319037134
Keyword(s)1. ALGEBRAIC TOPOLOGY 2. EBOOK 3. EBOOK - SPRINGER 4. FUNCTIONAL ANALYSIS 5. Mathematical Methods in Physics 6. PHYSICS
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TitleAn Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces
Author(s)Schlichenmaier, Martin
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2007.
DescriptionXIII, 217 p : online resource
ISBN,Price9783540711759
Keyword(s)1. ALGEBRAIC TOPOLOGY 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. MATHEMATICAL PHYSICS 7. QUANTUM FIELD THEORY 8. Theoretical, Mathematical and Computational Physics
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TitleAlgebraic K-Theory: Connections with Geometry and Topology
Author(s)Jardine, John F;Snaith, V.P
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1989.
DescriptionXIV, 550 p : online resource
Abstract NoteA NATO Advanced Study Institute entitled "Algebraic K-theory: Connections with Geometry and Topology" was held at the Chateau Lake Louise, Lake Louise, Alberta, Canada from December 7 to December 11 of 1987. This meeting was jointly supported by NATO and the Natural Sciences and Engineering Research Council of Canada, and was sponsored in part by the Canadian Mathematical Society. This book is the volume of proceedings for that meeting. Algebraic K-theory is essentially the study of homotopy invariants arising from rings and their associated matrix groups. More importantly perhaps, the subject has become central to the study of the relationship between Topology, Algebraic Geometry and Number Theory. It draws on all of these fields as a subject in its own right, but it serves as well as an effective translator for the application of concepts from one field in another. The papers in this volume are representative of the current state of the subject. They are, for the most part, research papers which are primarily of interest to researchers in the field and to those aspiring to be such. There is a section on problems in this volume which should be of particular interest to students; it contains a discussion of the problems from Gersten's well-known list of 1973, as well as a short list of new problems
ISBN,Price9789400923997
Keyword(s)1. ALGEBRAIC GEOMETRY 2. ALGEBRAIC TOPOLOGY 3. EBOOK 4. EBOOK - SPRINGER 5. K-THEORY
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TitleAlgebraic K-Theory and Algebraic Topology
Author(s)Goerss, P.G;Jardine, John F
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1993.
DescriptionXII, 328 p : online resource
Abstract NoteA NATO Advanced Study Institute entitled "Algebraic K-theory and Algebraic Topology" was held at Chateau Lake Louise, Lake Louise, Alberta, Canada from December 12 to December 16 of 1991. This book is the volume of proceedings for this meeting. The papers that appear here are representative of most of the lectures that were given at the conference, and therefore present a "snapshot" of the state ofthe K-theoretic art at the end of 1991. The underlying objective of the meeting was to discuss recent work related to the Lichtenbaum-Quillen complex of conjectures, fro~ both the algebraic and topological points of view. The papers in this volume deal with a range of topics, including motivic cohomology theories, cyclic homology, intersection homology, higher class field theory, and the former telescope conjecture. This meeting was jointly funded by grants from NATO and the National Science Foun?? dation in the United States. I would like to take this opportunity to thank these agencies for their support. I would also like to thank the other members of the organizing com?? mittee, namely Paul Goerss, Bruno Kahn and Chuck Weibel, for their help in making the conference successful. This was the second NATO Advanced Study Institute to be held in this venue; the first was in 1987. The success of both conferences owes much to the professionalism and helpfulness of the administration and staff of Chateau Lake Louise
ISBN,Price9789401706957
Keyword(s)1. ALGEBRA 2. ALGEBRAIC GEOMETRY 3. ALGEBRAIC TOPOLOGY 4. Associative rings 5. Associative Rings and Algebras 6. EBOOK 7. EBOOK - SPRINGER 8. K-THEORY 9. Order, Lattices, Ordered Algebraic Structures 10. Ordered algebraic structures 11. Rings (Algebra)
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TitleAn Introduction to Riemann Surfaces, Algebraic Curves and Moduli Spaces
Author(s)Schlichenmaier, Martin
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 1989.
DescriptionXIII, 149 p : online resource
Abstract NoteThis lecture is intended as an introduction to the mathematical concepts of algebraic and analytic geometry. It is addressed primarily to theoretical physicists, in particular those working in string theories. The author gives a very clear exposition of the main theorems, introducing the necessary concepts by lucid examples, and shows how to work with the methods of algebraic geometry. As an example he presents the Krichever-Novikov construction of algebras of Virasaro type. The book will be welcomed by many researchers as an overview of an important branch of mathematics, a collection of useful formulae and an excellent guide to the more extensive mathematical literature
ISBN,Price9783540459347
Keyword(s)1. ALGEBRAIC GEOMETRY 2. ALGEBRAIC TOPOLOGY 3. EBOOK 4. EBOOK - SPRINGER 5. Elementary particles (Physics) 6. Elementary Particles, Quantum Field Theory 7. MATHEMATICAL PHYSICS 8. QUANTUM FIELD THEORY 9. Theoretical, Mathematical and Computational Physics
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