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1 Rejzner, Kasia Perturbative Algebraic Quantum Field Theory I10180 2016 eBook  
2 Levi, Decio Symmetries and Integrability of Difference Equations I10153 2017 eBook  
3 Tanaka, Akinori Superconformal Index on RP2 ?? S1 and 3D Mirror Symmetry I09758 2016 eBook  
4 Dappiaggi, Claudio Hadamard States from Light-like Hypersurfaces I09659 2017 eBook  
5 Gordon, B. Brent The Arithmetic and Geometry of Algebraic Cycles I10736 2000 eBook  
6 Arodz, Henryk Lectures on Classical and Quantum Theory of Fields I07143 2010 eBook  
7 Nair, V. P Quantum Field Theory I06699 2005 eBook  
8 Smirnov, Vladimir A Analytic Tools for Feynman Integrals I06128 2012 eBook  
9 Maia, M. D Geometry of the Fundamental Interactions I05463 2011 eBook  
10 Barlotti, A Generators and Relations in Groups and Geometries I02261 1991 eBook  
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TitlePerturbative Algebraic Quantum Field Theory : An Introduction for Mathematicians
Author(s)Rejzner, Kasia
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2016.
DescriptionXI, 180 p. 4 illus : online resource
Abstract NotePerturbative Algebraic Quantum Field Theory (pAQFT), the subject of this book, is a complete and mathematically rigorous treatment of perturbative quantum field theory (pQFT) that doesn???t require the use of divergent quantities. We discuss in detail the examples of scalar fields and gauge theories and generalize them to QFT on curved spacetimes. pQFT models describe a wide range of physical phenomena and have remarkable agreement with experimental results. Despite this success, the theory suffers from many conceptual problems. pAQFT is a good candidate to solve many, if not all of these conceptual problems. Chapters 1-3 provide some background in mathematics and physics. Chapter 4 concerns classical theory of the scalar field, which is subsequently quantized in chapters 5 and 6. Chapter 7 covers gauge theory and chapter 8 discusses QFT on curved spacetimes and effective quantum gravity. The book aims to be accessible researchers and graduate students interested in the mathematical foundations of pQFT are the intended audience
ISBN,Price9783319259017
Keyword(s)1. ALGEBRA 2. EBOOK 3. EBOOK - SPRINGER 4. Field theory (Physics) 5. Field Theory and Polynomials 6. MATHEMATICAL PHYSICS 7. Quantum Field Theories, String Theory 8. QUANTUM FIELD THEORY 9. STRING THEORY
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TitleSymmetries and Integrability of Difference Equations : Lecture Notes of the Abecederian School of SIDE 12, Montreal 2016
Author(s)Levi, Decio;Rebelo, Rapha??l;Winternitz, Pavel
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionX, 435 p. 67 illus., 26 illus. in color : online resource
Abstract NoteThis book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers
ISBN,Price9783319566665
Keyword(s)1. ALGEBRA 2. Difference and Functional Equations 3. DIFFERENCE EQUATIONS 4. EBOOK 5. EBOOK - SPRINGER 6. Field theory (Physics) 7. Field Theory and Polynomials 8. FUNCTIONAL EQUATIONS 9. Numerical and Computational Physics, Simulation 10. PHYSICS
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TitleSuperconformal Index on RP2 ?? S1 and 3D Mirror Symmetry
Author(s)Tanaka, Akinori
PublicationSingapore, 1. Imprint: Springer 2. Springer Singapore, 2016.
DescriptionXII, 83 p : online resource
Abstract NoteThe author introduces the supersymmetric localization technique, a new approach for computing path integrals in quantum field theory on curved space (time) defined with interacting Lagrangian. The author focuses on a particular quantity called the superconformal index (SCI), which is defined by considering the theories on the product space of two spheres and circles, in order to clarify the validity of so-called three-dimensional mirror symmetry, one of the famous duality proposals. In addition to a review of known results, the author presents a new definition of SCI by considering theories on the product space of real-projective space and circles. In this book, he explains the concept of SCI from the point of view of quantum mechanics and gives localization computations by reducing field theoretical computations to many-body quantum mechanics. He applies his new results of SCI with real-projective space to test three-dimensional mirror symmetry, one of the dualities of quantum field theory. Real-projective space is known to be an unorientable surface like the Mobius strip, and there are many exotic effects resulting from Z2 holonomy of the surface. Thanks to these exotic structures, his results provide completely new evidence of three-dimensional mirror symmetry. The equivalence expected from three-dimensional mirror symmetry is transformed into a conjectural non-trivial mathematical identity through the new SCI, and he performs the proof of the identity using a q-binomial formula
ISBN,Price9789811013980
Keyword(s)1. ALGEBRA 2. EBOOK 3. EBOOK - SPRINGER 4. Field theory (Physics) 5. Field Theory and Polynomials 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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TitleHadamard States from Light-like Hypersurfaces
Author(s)Dappiaggi, Claudio;Moretti, Valter;Pinamonti, Nicola
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionVIII, 106 p. 2 illus : online resource
Abstract NoteThis book provides a rather self-contained survey of the construction of Hadamard states for scalar field theories in a large class of notable spacetimes, possessing a (conformal) light-like boundary. The first two sections focus on explaining a few introductory aspects of this topic and on providing the relevant geometric background material. The notions of asymptotically flat spacetimes and of expanding universes with a cosmological horizon are analysed in detail, devoting special attention to the characterization of asymptotic symmetries. In the central part of the book, the quantization of a real scalar field theory on such class of backgrounds is discussed within the framework of algebraic quantum field theory. Subsequently it is explained how it is possible to encode the information of the observables of the theory in a second, ancillary counterpart, which is built directly on the conformal (null) boundary. This procedure, dubbed bulk-to-boundary correspondence, has the net advantage of allowing the identification of a distinguished state for the theory on the boundary, which admits a counterpart in the bulk spacetime which is automatically of Hadamard form. In the last part of the book, some applications of these states are discussed, in particular the construction of the algebra of Wick polynomials. This book is aimed mainly, but not exclusively, at a readership with interest in the mathematical formulation of quantum field theory on curved backgrounds
ISBN,Price9783319643434
Keyword(s)1. ALGEBRA 2. COSMOLOGY 3. EBOOK 4. EBOOK - SPRINGER 5. Field theory (Physics) 6. Field Theory and Polynomials 7. MATHEMATICAL PHYSICS 8. Quantum Field Theories, String Theory 9. QUANTUM FIELD THEORY 10. STRING THEORY
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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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TitleLectures on Classical and Quantum Theory of Fields
Author(s)Arodz, Henryk;Hadasz, Leszek
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2010.
DescriptionIX, 351 p : online resource
Abstract NoteThis textbook on classical and quantum theory of fields addresses graduate students starting to specialize in theoretical physics. It provides didactic introductions to the main topics in the theory of fields, while taking into account the contemporary view of the subject. The student will find concise explanations of basic notions essential for applications of the theory of fields as well as for frontier research in theoretical physics. One third of the book is devoted to classical fields. Each chapter contains exercises of varying degree of difficulty with hints or solutions, plus summaries and worked examples as useful. The textbook is based on lectures delivered to students of theoretical physics at Jagiellonian University. It aims to deliver a unique combination of classical and quantum field theory in one compact course
ISBN,Price9783642156243
Keyword(s)1. ALGEBRA 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. Field theory (Physics) 7. Field Theory and Polynomials 8. QUANTUM FIELD THEORY 9. QUANTUM PHYSICS
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TitleQuantum Field Theory : A Modern Perspective
Author(s)Nair, V. P
PublicationNew York, NY, 1. Imprint: Springer 2. Springer New York, 2005.
DescriptionXIV, 558 p. 100 illus : online resource
Abstract NoteQuantum field theory, which started with Paul Dirac???s work shortly after the discovery of quantum mechanics, has produced an impressive and important array of results. Quantum electrodynamics, with its extremely accurate and well-tested predictions, and the standard model of electroweak and chromodynamic (nuclear) forces are examples of successful theories. Field theory has also been applied to a variety of phenomena in condensed matter physics, including superconductivity, superfluidity and the quantum Hall effect. The concept of the renormalization group has given us a new perspective on field theory in general and on critical phenomena in particular. At this stage, a strong case can be made that quantum field theory is the mathematical and intellectual framework for describing and understanding all physical phenomena, except possibly for a quantum theory of gravity. Quantum Field Theory: A Modern Perspective presents Professor Nair???s view of certain topics in field theory loosely knit together as it grew out of courses on field theory and particle physics taught at Columbia University and the City College of CUNY. The first few chapters, up to Chapter 12, contain material that generally goes into any course on quantum field theory, although there are a few nuances of presentation which readers may find to be different from other books. This first part of the book can be used for a general course on field theory, omitting, perhaps, the last three sections in Chapter 3, the last two in Chapter 8 and sections 6 and 7 in Chapter 10. The remaining chapters cover some of the more modern developments over the last three decades, involving topological and geometrical features. The introduction given to the mathematical basis of this part of the discussion is necessarily brief and should be accompanied by books on the relevant mathematical topics as indicated in the bibliography. Professor Nair also concentrates on developments pertinent to a better understanding of the standard model. There is no discussion of supersymmetry, supergravity, developments in field theory inspired by string theory, etc. There is also no detailed discussion of the renormalization group. Each of these topics would require a book in its own right to do justice to the topic. Quantum Field Theory: A Modern Perspective serves as a portal to so many more topics of detailed and ongoing research, referring readers to more detailed treatments for many specific topics. The book also contains extensive references, providing readers a more comprehensive perspective on the literature and the historical development of the subject. V. Parameswaran Nair is Professor of Physics at City College of The City University of New York (CUNY). Professor Nair has held Visiting Professorships at The Abdus Salam International Center for Theoretical Physics, Rockefeller University, Institute for Advanced Study at Princeton, and Massachusetts Institute of Technology
ISBN,Price9780387250984
Keyword(s)1. ALGEBRA 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. Field theory (Physics) 7. Field Theory and Polynomials 8. Mathematical Methods in Physics 9. PHYSICS 10. QUANTUM FIELD THEORY 11. QUANTUM PHYSICS
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TitleAnalytic Tools for Feynman Integrals
Author(s)Smirnov, Vladimir A
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2012.
DescriptionX, 298 p : online resource
Abstract NoteThe goal of this book is to describe the most powerful methods for evaluating multiloop Feynman integrals that are currently used in practice.?? This book supersedes the author???s previous Springer book ???Evaluating Feynman Integrals??? and its textbook version ???Feynman Integral Calculus.??? Since the publication of these two books, powerful new methods have arisen and conventional methods have been improved on in essential ways. A further qualitative change is the fact that most of the methods and the corresponding algorithms have now been implemented in computer codes which are often public. In comparison to the two previous books, three new chapters have been added:?? One is on sector decomposition, while the second describes a new method by Lee. The third new chapter concerns the asymptotic expansions of Feynman integrals in momenta and masses, which were described in detail in another Springer book, ???Applied Asymptotic Expansions in Momenta and Masses,??? by the author. This chapter describes, on the basis of papers that appeared after the publication of said book, how to algorithmically discover the regions relevant to a given limit within the strategy of expansion by regions. In addition, the chapters on the method of Mellin-Barnes representation and on the method of integration by parts have been substantially rewritten, with an emphasis on the corresponding algorithms and computer codes
ISBN,Price9783642348860
Keyword(s)1. ALGEBRA 2. EBOOK 3. EBOOK - SPRINGER 4. Field theory (Physics) 5. Field Theory and Polynomials 6. NUCLEAR PHYSICS 7. Numerical and Computational Physics, Simulation 8. Particle and Nuclear Physics 9. PHYSICS 10. QUANTUM PHYSICS
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TitleGeometry of the Fundamental Interactions : On Riemann's Legacy to High Energy Physics and Cosmology
Author(s)Maia, M. D
PublicationNew York, NY, 1. Imprint: Springer 2. Springer New York, 2011.
DescriptionIX, 179 p : online resource
Abstract NoteGravitation, electromagnetics and the two types of nuclear forces constitute the four fundamental forces of nature which regulate our everyday life.?? Amazingly, they are all described by a single idea of the 19th century proposed by Bernhard Riemann, and with the exception of??gravitation, these ideas have been since confirmed by high energy experiments and cosmological observations.?? Geometry of the Fundamental Interactions - On Riemann's Legacy to High Energy Physics and Cosmology is a mathematical narrative of how we have come to agree on such a complex plot of nature, starting with the basic geometrical concepts and ending with hints on the perspective for cosmology. This book originated from lectures given for several years to a mixed audience of mathematicians, physicists, astronomers, engineers, philosophers and sociologists seeking to understand the basics of those interactions and how the concept of Riemann curvature came to occupy such a central position in physics.?? The author takes on the challenge of making the path toward understanding both accessible and interesting to a wide audience
ISBN,Price9781441982735
Keyword(s)1. ALGEBRA 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. Field theory (Physics) 7. Field Theory and Polynomials 8. GEOMETRY 9. MATHEMATICAL PHYSICS 10. QUANTUM FIELD THEORY 11. Theoretical, Mathematical and Computational Physics
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TitleGenerators and Relations in Groups and Geometries
Author(s)Barlotti, A;Ellers, E.W;Plaumann, P;Strambach, K
PublicationDordrecht, 1. Imprint: Springer 2. Springer Netherlands, 1991.
DescriptionXV, 447 p : online resource
Abstract NoteEvery group is represented in many ways as an epimorphic image of a free group. It seems therefore futile to search for methods involving generators and relations which can be used to detect the structure of a group. Nevertheless, results in the indicated direction exist. The clue is to ask the right question. Classical geometry is a typical example in which the factorization of a motion into reflections or, more generally, of a collineation into central collineations, supplies valuable information on the geometric and algebraic structure. This mode of investigation has gained momentum since the end of last century. The tradition of geometric-algebraic interplay brought forward two branches of research which are documented in Parts I and II of these Proceedings. Part II deals with the theory of reflection geometry which culminated in Bachmann's work where the geometric information is encoded in properties of the group of motions expressed by relations in the generating involutions. This approach is the backbone of the classification of motion groups for the classical unitary and orthogonal planes. The axioms in this char?? acterization are natural and plausible. They provoke the study of consequences of subsets of axioms which also yield natural geometries whose exploration is rewarding. Bachmann's central axiom is the three reflection theorem, showing that the number of reflections needed to express a motion is of great importance
ISBN,Price9789401133821
Keyword(s)1. ALGEBRA 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. Field theory (Physics) 6. Field Theory and Polynomials 7. GROUP THEORY 8. Group Theory and Generalizations 9. Linear and Multilinear Algebras, Matrix Theory 10. MATRIX THEORY
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