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1 Bountis, Tassos Chaos, Fractals and Complexity I12832 2023 eBook  
2 Deshko, Yury Special Relativity I12503 2022 Book  
3 Finn, Kieran Geometric Approaches to Quantum Field Theory I11853 2021 eBook  
4 Dierck-Ekkehard Liebscher Geometry of time OB1822 2005 eBook  
5 Dribus, Benjamin F Discrete Causal Theory I10462 2017 eBook  
6 Graf-Grossmann, Claudia Marcel Grossmann I09808 2018 eBook  
7 Landi, Giovanni Linear Algebra and Analytic Geometry for Physical Sciences I09687 2018 eBook  
8 Osterhage, Wolfgang Johannes Kepler I08807 2020 eBook  
9 Lionni, Luca Colored Discrete Spaces I08748 2018 eBook  
10 Vozmischeva, T.G Integrable Problems of Celestial Mechanics in Spaces of Constant Curvature I11314 2003 eBook  
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TitleChaos, Fractals and Complexity
Author(s)Bountis, Tassos;Vallianatos, Filippos;Provata, Astero;Kugiumtzis, Dimitris;Kominis, Yannis
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2023.
DescriptionXXV, 374 p. 102 illus., 85 illus. in color : online resource
Abstract NoteThis volume of proceedings contains research results within the framework of the fields of Chaos, Fractals and Complexity, written by experienced professors, young researchers, and applied scientists. It includes reviews of the fields, which are presented in an educational way for the widest possible audience, analytical results, computer simulations and experimental evidence, focusing on mathematical modelling. The papers presented here are selected from lectures given at the 28th Summer School ???Dynamical Systems and Complexity???, July 18 ??? 27, 2022. Topics cover applications of complex systems in Neuroscience, Biology, Photonics, Seismology, Meteorology, and more broadly Physical and Engineering systems. The summer school has a long history, which began at the University of Patras in 1987 and continues with great success to this day. The original main purpose was to introduce young students and researchers of Greece to a new science that emerged several decades ago and continues to grow internationally at an ever increasing rate around the world
ISBN,Price9783031374043
Keyword(s)1. Applied Dynamical Systems 2. COMPLEX SYSTEMS 3. Computational neuroscience 4. DYNAMICS 5. EBOOK - SPRINGER 6. GEOMETRY 7. NONLINEAR THEORIES 8. SYSTEM THEORY
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2.     
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TitleSpecial Relativity : For Inquiring Minds
Author(s)Deshko, Yury
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2022.
DescriptionXIV, 348 p. 177 illus., 137 illus. in color : online resource
Abstract NoteThis textbook introduces the special theory of relativity at a level which is accessible to undergraduate students and even high school students with a strong foundation in algebra. The presentation emphasizes clean algebraic and geometrical methods, visualized with plenty of illustrations, resulting in a textbook that is modern and serious yet accessible. Replete with many solved exercises and copious spacetime diagrams, this book will help students develop relativistic intuition when encountering the subject for the first time. The emphasis on geometric methods, combined with the pedagogically appealing k-calculus approach, makes this book ideal for a self-contained course on special relativity or as supplementary reading for modern physics courses. It will also appeal to high schoolers with a strong math background who want to get ahead
ISBN,Price9783030911423
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GEOMETRY 4. GRAVITATION 5. GRAVITATIONAL PHYSICS 6. SPECIAL RELATIVITY 7. Special relativity (Physics)
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TitleGeometric Approaches to Quantum Field Theory
Author(s)Finn, Kieran
PublicationCham, Springer International Publishing, 2021.
DescriptionXIX, 202 p. 7 illus., 6 illus. in color : online resource
Abstract NoteThe ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself. The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin ?? and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe. This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory
ISBN,Price9783030852696
Keyword(s)1. Classical and Quantum Gravity 2. COSMOLOGY 3. EBOOK 4. EBOOK - SPRINGER 5. Elementary particles (Physics) 6. Elementary Particles, Quantum Field Theory 7. GEOMETRY 8. GRAVITATION 9. QUANTUM FIELD THEORY
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4.     
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TitleGeometry of time
Author(s)Dierck-Ekkehard Liebscher
PublicationVerlag, John Wiley and Sons, 2005.
Abstract NoteA description of the geometry of space-time with all the questions and issues explained without the need for formulas. As such, the author shows that this is indeed geometry, with actual constructions familiar from Euclidean geometry, and which allow exact demonstrations and proofs. The formal mathematics behind these constructions is provided in the appendices. The result is thus not a textbook introducing readers to the theory of special relativity so they may calculate formally, but rather aims to show the connection with synthetic geometry. It presents the relation to projective geometry and uses this to illustrate the starting points of general relativity. Written at an introductory level for undergraduates, this novel presentation will also benefit teaching staff.
ISBN,Price9783527405671 : $ 145.00(Online)
Keyword(s)1. EBOOK 2. EBOOK - WILEY 3. GEOMETRIES OF THE PLAN 4. GEOMETRY 5. RELATIVITY THEORY 6. SPACE AND TIME
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TitleDiscrete Causal Theory : Emergent Spacetime and the Causal Metric Hypothesis
Author(s)Dribus, Benjamin F
PublicationCham, Springer International Publishing, 2017.
DescriptionXXX, 558 p. 154 illus : online resource
Abstract NoteThis book evaluates and suggests potentially critical improvements to causal set theory, one of the best-motivated approaches to the outstanding problems of fundamental physics. Spacetime structure is of central importance to physics beyond general relativity and the standard model. The causal metric hypothesis treats causal relations as the basis of this structure. The book develops the consequences of this hypothesis under the assumption of a fundamental scale, with smooth spacetime geometry viewed as emergent. This approach resembles causal set theory, but differs in important ways; for example, the relative viewpoint, emphasizing relations between pairs of events, and relationships between pairs of histories, is central. The book culminates in a dynamical law for quantum spacetime, derived via generalized path summation
ISBN,Price9783319500836
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. COSMOLOGY 3. EBOOK 4. EBOOK - SPRINGER 5. GEOMETRY 6. GRAVITATION 7. TOPOLOGY
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6.     
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TitleMarcel Grossmann : For the Love of Mathematics
Author(s)Graf-Grossmann, Claudia
PublicationCham, Springer International Publishing, 2018.
DescriptionXVIII, 263 p. 91 illus., 1 illus. in color : online resource
Abstract NoteZurich, summer 1912. Albert Einstein has just returned from Prague to the city on the Limmat. He sends a plea for help to his former fellow student, the mathematician Marcel Grossmann (1878-1936), for he is in need of assistance with the mathematical calculations of his general theory of relativity. What then follows is one of the most fascinating chapters of science history, with far-reaching consequences for the lives of the two friends. Marcel Grossmann???s granddaughter paints here a picture of a fiery and many-talented scientist and patriot. She traces the influence of an entrepreneurial family during Germany???s rapid industrial expansion in the late 19th century. The family???s fluctuating fortunes take the story to the vibrant city of Budapest on the Danube; they enable readers to sense the pioneering spirit at Zurich???s young Polytechnic Institute (now ETH Zurich) ??? but also reflect the worries and hardships of the First World War and interwar years. The Foreword is written by Prof. Remo Ruffini, founder and president of the International Center for Relativistic Astrophysics and the Marcel Grossmann Meetings. Last but not least, an extensive contribution by Dr. Tilman Sauer offers a scientific-historical appreciation of Marcel Grossmann???s enduring contributions
ISBN,Price9783319900773
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. EBOOK 3. EBOOK - SPRINGER 4. Europe, Central???History 5. GEOMETRY 6. GRAVITATION 7. History and Philosophical Foundations of Physics 8. History of Germany and Central Europe 9. MATHEMATICS 10. PHYSICS 11. Popular Science in Mathematics 12. Popular Science in Physics
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7.     
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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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8.     
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TitleJohannes Kepler : The Order of Things
Author(s)Osterhage, Wolfgang
PublicationCham, Springer International Publishing, 2020.
DescriptionIX, 132 p. 24 illus., 10 illus. in color : online resource
Abstract NoteThis book traces the development of Kepler???s ideas along with his unsteady wanderings in a world dominated by religious turmoil. Johannes Kepler, like Galileo, was a supporter of the Copernican heliocentric world model. From an early stage, his principal objective was to discover ???the world behind the world???, i.e. to identify the underlying order and the secrets that make the world function as it does: the hidden world harmony. Kepler was driven both by his religious belief and Greek mysticism, which he found in ancient mathematics. His urge to find a construct encompassing the harmony of every possible aspect of the world ??? including astronomy, geometry and music ??? is seen as a manifestation of a deep human desire to bring order to the apparent chaos surrounding our existence. This desire continues to this day as we search for a theory that will finally unify and harmonise the forces of nature
ISBN,Price9783030468583
Keyword(s)1. ASTRONOMY 2. Astronomy, Astrophysics and Cosmology 3. ASTROPHYSICS 4. EBOOK 5. EBOOK - SPRINGER 6. GEOMETRY 7. History and Philosophical Foundations of Physics 8. PHYSICS 9. Popular Science in Astronomy
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9.     
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TitleColored Discrete Spaces : Higher Dimensional Combinatorial Maps and Quantum Gravity
Author(s)Lionni, Luca
PublicationCham, Springer International Publishing, 2018.
DescriptionXVIII, 218 p. 107 illus., 98 illus. in color : online resource
Abstract NoteThis book provides a number of combinatorial tools that allow a systematic study of very general discrete spaces involved in the context of discrete quantum gravity. In any dimension D, we can discretize Euclidean gravity in the absence of matter over random discrete spaces obtained by gluing families of polytopes together in all possible ways. These spaces are then classified according to their curvature. In D=2, it results in a theory of random discrete spheres, which converge in the continuum limit towards the Brownian sphere, a random fractal space interpreted as a quantum random space-time. In this limit, the continuous Liouville theory of D=2 quantum gravity is recovered. Previous results in higher dimension regarded triangulations, converging towards a continuum random tree, or gluings of simple building blocks of small sizes, for which multi-trace matrix model results are recovered in any even dimension. In this book, the author develops a bijection with stacked two-dimensional discrete surfaces for the most general colored building blocks, and details how it can be used to classify colored discrete spaces according to their curvature. The way in which this combinatorial problem arrises in discrete quantum gravity and random tensor models is discussed in detail
ISBN,Price9783319960234
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. EBOOK 3. EBOOK - SPRINGER 4. GEOMETRY 5. GRAVITATION 6. Mathematical Methods in Physics 7. PHYSICS
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10.    
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TitleIntegrable Problems of Celestial Mechanics in Spaces of Constant Curvature
Author(s)Vozmischeva, T.G
PublicationDordrecht, Springer Netherlands, 2003.
DescriptionXI, 184 p : online resource
Abstract NoteIntrod uction The problem of integrability or nonintegrability of dynamical systems is one of the central problems of mathematics and mechanics. Integrable cases are of considerable interest, since, by examining them, one can study general laws of behavior for the solutions of these systems. The classical approach to studying dynamical systems assumes a search for explicit formulas for the solutions of motion equations and then their analysis. This approach stimulated the development of new areas in mathematics, such as the al?? gebraic integration and the theory of elliptic and theta functions. In spite of this, the qualitative methods of studying dynamical systems are much actual. It was Poincare who founded the qualitative theory of differential equa?? tions. Poincare, working out qualitative methods, studied the problems of celestial mechanics and cosmology in which it is especially important to understand the behavior of trajectories of motion, i.e., the solutions of differential equations at infinite time. Namely, beginning from Poincare systems of equations (in connection with the study of the problems of ce?? lestial mechanics), the right-hand parts of which don't depend explicitly on the independent variable of time, i.e., dynamical systems, are studied
ISBN,Price9789401703031
Keyword(s)1. Astronomy, Observations and Techniques 2. Astronomy???Observations 3. EBOOK 4. EBOOK - SPRINGER 5. GEOMETRY 6. Observations, Astronomical
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