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1 Bedford, Anthony Hamilton???s Principle in Continuum Mechanics I11933 2021 eBook  
2 Stacey, Blake C A First Course in the Sporadic SICs I11815 2021 eBook  
3 Timberlake, Todd Keene Classical Mechanics with Maxima I10330 2016 eBook  
4 Rejzner, Kasia Perturbative Algebraic Quantum Field Theory I10180 2016 eBook  
5 Levi, Decio Symmetries and Integrability of Difference Equations I10153 2017 eBook  
6 Tanaka, Akinori Superconformal Index on RP2 ?? S1 and 3D Mirror Symmetry I09758 2016 eBook  
7 Landi, Giovanni Linear Algebra and Analytic Geometry for Physical Sciences I09687 2018 eBook  
8 Dappiaggi, Claudio Hadamard States from Light-like Hypersurfaces I09659 2017 eBook  
9 Konno, Hitoshi Elliptic Quantum Groups I09584 2020 eBook  
10 Weingartner, Paul A Alternative Logics. Do Sciences Need Them? I11584 2004 eBook  
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TitleHamilton???s Principle in Continuum Mechanics
Author(s)Bedford, Anthony
PublicationCham, Springer International Publishing, 2021.
DescriptionXIV, 104 p. 16 illus : online resource
Abstract NoteThis revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton???s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton???s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces. Presents a comprehensive, rigorous description of the application of Hamilton???s principle to continuous media; Includes recent applications of the principle to continua with microstructure, mixtures, and media with surfaces of discontinuity; Discusses foundations of continuum mechanics and variational methods therein in the context of linear vector spaces
ISBN,Price9783030903060
Keyword(s)1. ALGEBRA 2. CALCULUS OF VARIATIONS 3. Calculus of Variations and Optimization 4. Classical and Continuum Physics 5. CONTINUUM MECHANICS 6. EBOOK 7. EBOOK - SPRINGER 8. ENGINEERING MECHANICS 9. MATHEMATICAL OPTIMIZATION 10. MATHEMATICAL PHYSICS 11. Mechanics, Applied 12. PHYSICS
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TitleA First Course in the Sporadic SICs
Author(s)Stacey, Blake C
PublicationCham, Springer International Publishing, 2021.
DescriptionVIII, 115 p. 7 illus., 2 illus. in color : online resource
Abstract NoteThis book focuses on the Symmetric Informationally Complete quantum measurements (SICs) in dimensions 2 and 3, along with one set of SICs in dimension 8. These objects stand out in ways that have earned them the moniker of "sporadic SICs". By some standards, they are more approachable than the other known SICs, while by others they are simply atypical. The author forays into quantum information theory using them as examples, and the author explores their connections with other exceptional objects like the Leech lattice and integral octonions. The sporadic SICs take readers from the classification of finite simple groups to Bell's theorem and the discovery that "hidden variables" cannot explain away quantum uncertainty. While no one department teaches every subject to which the sporadic SICs pertain, the topic is approachable without too much background knowledge. The book includes exercises suitable for an elective at the graduate or advanced undergraduate level
ISBN,Price9783030761042
Keyword(s)1. ALGEBRA 2. EBOOK 3. EBOOK - SPRINGER 4. GROUP THEORY 5. Group Theory and Generalizations 6. Order, Lattices, Ordered Algebraic Structures 7. Quantum computing 8. QUANTUM INFORMATION
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TitleClassical Mechanics with Maxima
Author(s)Timberlake, Todd Keene;Mixon, J. Wilson
PublicationNew York, NY, Springer New York, 2016.
DescriptionXI, 258 p. 156 illus : online resource
Abstract NoteThis book guides undergraduate students in the use of Maxima???a computer algebra system???in solving problems in classical mechanics. It functions well as a supplement to a typical classical mechanics textbook. When it comes to problems that are too difficult to solve by hand, computer algebra systems that can perform symbolic mathematical manipulations are a valuable tool. Maxima is particularly attractive in that it is open-source, multiple-platform software that students can download and install free of charge. Lessons learned and capabilities developed using Maxima are easily transferred to other, proprietary software
ISBN,Price9781493932078
Keyword(s)1. ALGEBRA 2. CLASSICAL MECHANICS 3. Computational Mathematics and Numerical Analysis 4. Computer mathematics 5. EBOOK 6. EBOOK - SPRINGER 7. General Algebraic Systems 8. Mathematical Applications in the Physical Sciences 9. Mathematical Methods in Physics 10. MATHEMATICAL PHYSICS 11. MECHANICS 12. PHYSICS
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TitlePerturbative Algebraic Quantum Field Theory : An Introduction for Mathematicians
Author(s)Rejzner, Kasia
PublicationCham, 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, 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, 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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TitleLinear Algebra and Analytic Geometry for Physical Sciences
Author(s)Landi, Giovanni;Zampini, Alessandro
PublicationCham, Springer International Publishing, 2018.
DescriptionXII, 345 p : online resource
Abstract NoteA self-contained introduction to finite dimensional vector spaces, matrices, systems of linear equations, spectral analysis on euclidean and hermitian spaces, affine euclidean geometry, quadratic forms and conic sections. The mathematical formalism is motivated and introduced by problems from physics, notably mechanics (including celestial) and electro-magnetism, with more than two hundreds examples and solved exercises. Topics include: The group of orthogonal transformations on euclidean spaces, in particular rotations, with Euler angles and angular velocity. The rigid body with its inertia matrix. The unitary group. Lie algebras and exponential map. The Dirac???s bra-ket formalism. Spectral theory for self-adjoint endomorphisms on euclidean and hermitian spaces. The Minkowski spacetime from special relativity and the Maxwell equations. Conic sections with the use of eccentricity and Keplerian motions. An appendix collects basic algebraic notions like group, ring and field; and complex numbers and integers modulo a prime number. The book will be useful to students taking a physics or engineer degree for a basic education as well as for students who wish to be competent in the subject and who may want to pursue a post-graduate qualification
ISBN,Price9783319783611
Keyword(s)1. ALGEBRA 2. APPLIED MATHEMATICS 3. Computer science???Mathematics 4. EBOOK 5. EBOOK - SPRINGER 6. ENGINEERING MATHEMATICS 7. GEOMETRY 8. Linear and Multilinear Algebras, Matrix Theory 9. Math Applications in Computer Science 10. Mathematical and Computational Engineering 11. Mathematical Applications in the Physical Sciences 12. Mathematical Methods in Physics 13. MATHEMATICAL PHYSICS 14. MATRIX THEORY 15. PHYSICS
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TitleHadamard States from Light-like Hypersurfaces
Author(s)Dappiaggi, Claudio;Moretti, Valter;Pinamonti, Nicola
PublicationCham, 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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TitleElliptic Quantum Groups : Representations and Related Geometry
Author(s)Konno, Hitoshi
PublicationSingapore, Springer Singapore, 2020.
DescriptionXIII, 131 p. 3 illus : online resource
Abstract NoteThis is the first book on elliptic quantum groups, i.e., quantum groups associated to elliptic solutions of the Yang-Baxter equation. Based on research by the author and his collaborators, the book presents a comprehensive survey on the subject including a brief history of formulations and applications, a detailed formulation of the elliptic quantum group in the Drinfeld realization, explicit construction of both finite and infinite-dimensional representations, and a construction of the vertex operators as intertwining operators of these representations. The vertex operators are important objects in representation theory of quantum groups. In this book, they are used to derive the elliptic q-KZ equations and their elliptic hypergeometric integral solutions. In particular, the so-called elliptic weight functions appear in such solutions. The author???s recent study showed that these elliptic weight functions are identified with Okounkov???s elliptic stable envelopes for certain equivariant elliptic cohomology and play an important role to construct geometric representations of elliptic quantum groups. Okounkov???s geometric approach to quantum integrable systems is a rapidly growing topic in mathematical physics related to the Bethe ansatz, the Alday-Gaiotto-Tachikawa correspondence between 4D SUSY gauge theories and the CFT???s, and the Nekrasov-Shatashvili correspondences between quantum integrable systems and quantum cohomology. To invite the reader to such topics is one of the aims of this book
ISBN,Price9789811573873
Keyword(s)1. ALGEBRA 2. EBOOK 3. EBOOK - SPRINGER 4. GROUP THEORY 5. Group Theory and Generalizations 6. Mathematical Applications in the Physical Sciences 7. MATHEMATICAL PHYSICS 8. Order, Lattices, Ordered Algebraic Structures 9. Ordered algebraic structures
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TitleAlternative Logics. Do Sciences Need Them?
Author(s)Weingartner, Paul A
PublicationBerlin, Heidelberg, Springer Berlin Heidelberg, 2004.
DescriptionXVII, 368 p : online resource
Abstract NoteInitially proposed as rivals of classical logic, alternative logics have become increasingly important in sciences such as quantum physics, computer science, and artificial intelligence. The contributions collected in this volume address and explore the question whether the usage of logic in the sciences, especially in modern physics, requires a deviation from classical mathematical logic. The articles in the first part of the book set the scene by describing the context and the dilemma when applying logic in science. In Part II the authors offer several logics that deviate in different ways from classical logics. The twelve papers in Part III investigate in detail specific aspects such as quantum logic, quantum computation, computer-science considerations, praxic logic, and quantum probability. Most of the contributions are revised and partially extended versions of papers presented at a conference of the same title of the Acad??mie Internationale de Philosophie des Sciences held at the Internationales Forschungszentrum Salzburg in May 1999. Others have been added to complete the picture of recent research in alternative logics as they have been developed for applications in the sciences
ISBN,Price9783662056790
Keyword(s)1. ALGEBRA 2. COMPUTERS 3. EBOOK 4. EBOOK - SPRINGER 5. Order, Lattices, Ordered Algebraic Structures 6. Ordered algebraic structures 7. PHILOSOPHY 8. Philosophy, general 9. QUANTUM COMPUTERS 10. Quantum Information Technology, Spintronics 11. QUANTUM PHYSICS 12. SPINTRONICS 13. Theory of Computation
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