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1 Jany??ka, Josef An Introduction to Covariant Quantum Mechanics I12533 2022 Book  
2 Ludu, Andrei Nonlinear Waves and Solitons on Contours and Closed Surfaces I12309 2022 Book  
3 Liu, Chaoqun Liutex and Third Generation of Vortex Definition and Identification I11661 2021 eBook  
4 Kimura, Taro Instanton Counting, Quantum Geometry and Algebra I11645 2021 eBook  
5 Tristan Needham Visual differential geometry and forms: A Mathematical Drama in Five Acts 026961 2021 Book  
6 Rodrigues, Jr, Waldyr A The Many Faces of Maxwell, Dirac and Einstein Equations I10404 2016 eBook  
7 Fr??, Pietro Giuseppe Advances in Geometry and Lie Algebras from Supergravity I10019 2018 eBook  
8 Rowe, David E Beyond Einstein I09813 2018 eBook  
9 Rudolph, Gerd Differential Geometry and Mathematical Physics I09737 2017 eBook  
10 Lehmkuhl, Dennis Towards a Theory of Spacetime Theories I09130 2017 eBook  
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TitleAn Introduction to Covariant Quantum Mechanics
Author(s)Jany??ka, Josef;Modugno, Marco
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2022.
DescriptionXVIII, 838 p. 10 illus : online resource
Abstract NoteThis book deals with an original contribution to the hypothetical missing link unifying the two fundamental branches of physics born in the twentieth century, General Relativity and Quantum Mechanics. Namely, the book is devoted to a review of a "covariant approach" to Quantum Mechanics, along with several improvements and new results with respect to the previous related literature. The first part of the book deals with a covariant formulation of Galilean Classical Mechanics, which stands as a suitable background for covariant Quantum Mechanics. The second part deals with an introduction to covariant Quantum Mechanics. Further, in order to show how the presented covariant approach works in the framework of standard Classical Mechanics and standard Quantum Mechanics, the third part provides a detailed analysis of the standard Galilean space-time, along with three dynamical classical and quantum examples. The appendix accounts for several non-standard mathematical methods widely used in the body of the book
ISBN,Price9783030895891
Keyword(s)1. CLASSICAL MECHANICS 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. GEOMETRY, DIFFERENTIAL 6. MECHANICS 7. QUANTUM PHYSICS
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TitleNonlinear Waves and Solitons on Contours and Closed Surfaces
Author(s)Ludu, Andrei
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2022.
DescriptionXXXII, 566 p. 171 illus., 68 illus. in color : online resource
Abstract NoteThis new edition has been thoroughly revised, expanded and contain some updates function of the novel results and shift of scientific interest in the topics. The book has a Foreword by Jerry L. Bona and Hongqiu Chen. The book is an introduction to nonlinear waves and soliton theory in the special environment of compact spaces such a closed curves and surfaces and other domain contours. It assumes familiarity with basic soliton theory and nonlinear dynamical systems. The first part of the book introduces the mathematical concept required for treating the manifolds considered, providing relevant notions from topology and differential geometry. An introduction to the theory of motion of curves and surfaces - as part of the emerging field of contour dynamics - is given. The second and third parts discuss the modeling of various physical solitons on compact systems, such as filaments, loops and drops made of almost incompressible materials thereby intersecting with a large number of physical disciplines from hydrodynamics to compact object astrophysics. This book is intended for graduate students and researchers in mathematics, physics and engineering
ISBN,Price9783031146411
Keyword(s)1. Classical and Continuum Physics 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. GEOMETRY, DIFFERENTIAL 6. Mathematical Methods in Physics 7. MATHEMATICAL PHYSICS 8. PHYSICS 9. Soft and Granular Matter 10. Soft condensed matter 11. Surface and Interface and Thin Film 12. Surfaces (Physics)
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TitleLiutex and Third Generation of Vortex Definition and Identification : An Invited Workshop from Chaos 2020
Author(s)Liu, Chaoqun;Wang, Yiqian
PublicationCham, Springer International Publishing, 2021.
DescriptionXXXI, 468 p. 343 illus., 320 illus. in color : online resource
Abstract NoteThis book collects papers presented in the Invited Workshop, ???Liutex and Third Generation of Vortex Definition and Identification for Turbulence,??? from CHAOS2020, June 9-12, 2020, which was held online as a virtual conference. Liutex is a new physical quantity introduced by Prof. Chaoqun Liu of the University of Texas at Arlington. It is a vector and could give a unique and accurate mathematical definition for fluid rotation or vortex. The papers in this volume include some Liutex theories and many applications in hydrodynamics, aerodynamics and thermal dynamics including turbine machinery. As vortex exists everywhere in the universe, a mathematical definition of vortex or Liutex will play a critical role in scientific research. There is almost no place without vortex in fluid dynamics. As a projection, the Liutex theory will play an important role on the investigations of the vortex dynamics in hydrodynamics, aerodynamics, thermodynamics, oceanography, meteorology, metallurgy, civil engineering, astronomy, biology, etc. and to the researches of the generation, sustenance, modelling and controlling of turbulence
ISBN,Price9783030702175
Keyword(s)1. Aerospace engineering 2. Aerospace Technology and Astronautics 3. ASTRONAUTICS 4. DIFFERENTIAL GEOMETRY 5. EBOOK 6. EBOOK - SPRINGER 7. Engineering Fluid Dynamics 8. FLUID MECHANICS 9. FLUIDS 10. GEOMETRY, DIFFERENTIAL 11. PLASMA TURBULENCE 12. Soft condensed matter 13. Turbulence in plasmas
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TitleInstanton Counting, Quantum Geometry and Algebra
Author(s)Kimura, Taro
PublicationCham, Springer International Publishing, 2021.
DescriptionXXIII, 285 p. 36 illus., 13 illus. in color : online resource
Abstract NoteThis book pedagogically describes recent developments in gauge theory, in particular four-dimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the anti-self-dual Yang???Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg???Witten theory, together with string/M-theory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the ??-deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver W-algebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of W-algebra
ISBN,Price9783030761905
Keyword(s)1. ALGEBRAIC GEOMETRY 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. Elementary particles (Physics) 6. Elementary Particles, Quantum Field Theory 7. GEOMETRY, DIFFERENTIAL 8. MATHEMATICAL PHYSICS 9. QUANTUM FIELD THEORY
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TitleVisual differential geometry and forms: A Mathematical Drama in Five Acts
Author(s)Tristan Needham
PublicationUSA, Princeton University Press, 2021.
DescriptionPB : 584pp
Abstract NoteAn inviting, intuitive, and visual exploration of differential geometry and formsVisual Differential Geometry and Forms fulfills two principal goals. In the first four acts, Tristan Needham puts the geometry back into differential geometry. Using 235 hand-drawn diagrams, Needham deploys Newton’s geometrical methods to provide geometrical explanations of the classical results. In the fifth act, he offers the first undergraduate introduction to differential forms that treats advanced topics in an intuitive and geometrical manner.Unique features of the first four acts include: four distinct geometrical proofs of the fundamentally important Global Gauss-Bonnet theorem, providing a stunning link between local geometry and global topology; a simple, geometrical proof of Gauss’s famous Theorema Egregium; a complete geometrical treatment of the Riemann curvature tensor of an n-manifold; and a detailed geometrical treatment of Einstein’s field equation, describing gravity as curved spacetime (General Relativity), together with its implications for gravitational waves, black holes, and cosmology. The final act elucidates such topics as the unification of all the integral theorems of vector calculus; the elegant reformulation of Maxwell’s equations of electromagnetism in terms of 2-forms; de Rham cohomology; differential geometry via Cartan’s method of moving frames; and the calculation of the Riemann tensor using curvature 2-forms. Six of the seven chapters of Act V can be read completely independently from the rest of the book.Requiring only basic calculus and geometry, Visual Differential Geometry and Forms provocatively rethinks the way this important area of mathematics should be considered and taught.
ISBN,Price978-0691203706 : $ 45.00
Classification1. 514.7 NEE 2. 514.77 NEE 3. 517.7 NEE
Keyword(s)1. DIFFERENTIAL GEOMETRY 2. Forms 3. Geometry and Forms
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026961     Issued AP05: Prakash Arumugasamy 02/Sep/2023

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TitleThe Many Faces of Maxwell, Dirac and Einstein Equations : A Clifford Bundle Approach
Author(s)Rodrigues, Jr, Waldyr A;Capelas de Oliveira, Edmundo
PublicationCham, Springer International Publishing, 2016.
DescriptionXVI, 587 p. 14 illus : online resource
Abstract NoteThis book is an exposition of the algebra and calculus of differential forms, of the Clifford and Spin-Clifford bundle formalisms, and of vistas to a formulation of important concepts of differential geometry indispensable for an in-depth understanding of space-time physics. The formalism discloses the hidden geometrical nature of spinor fields. Maxwell, Dirac and Einstein fields are shown to have representatives by objects of the same mathematical nature, namely sections of an appropriate Clifford bundle. This approach reveals unity in diversity and suggests relationships that are hidden in the standard formalisms and opens new paths for research. This thoroughly revised second edition also adds three new chapters: on the Clifford bundle approach to the Riemannian or semi-Riemannian differential geometry of branes; on Komar currents in the context of the General Relativity theory; and an analysis of the similarities and main differences between Dirac, Majorana and ELKO spinor fields. The exercises with solutions, the comprehensive list of mathematical symbols, and the list of acronyms and abbreviations are provided for self-study for students as well as for classes. From the reviews of the first edition: ???The text is written in a very readable manner and is complemented with plenty of worked-out exercises which are in the style of extended examples. ... their book could also serve as a textbook for graduate students in physics or mathematics." (Alberto Molgado, Mathematical Reviews, 2008 k)
ISBN,Price9783319276373
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. GRAVITATION 6. Mathematical Applications in the Physical Sciences 7. MATHEMATICAL PHYSICS
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TitleAdvances in Geometry and Lie Algebras from Supergravity
Author(s)Fr??, Pietro Giuseppe
PublicationCham, Springer International Publishing, 2018.
DescriptionXX, 556 p. 64 illus., 32 illus. in color : online resource
Abstract NoteThis book aims to provide an overview of several topics in advanced Differential Geometry and Lie Group Theory, all of them stemming from mathematical problems in supersymmetric physical theories. It presents a mathematical illustration of the main development in geometry and symmetry theory that occurred under the fertilizing influence of supersymmetry/supergravity. The contents are mainly of mathematical nature, but each topic is introduced by historical information and enriched with motivations from high energy physics, which help the reader in getting a deeper comprehension of the subject.??
ISBN,Price9783319744919
Keyword(s)1. DIFFERENTIAL GEOMETRY 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. History and Philosophical Foundations of Physics 7. MATHEMATICAL PHYSICS 8. PHYSICS 9. QUANTUM FIELD THEORY 10. Theoretical, Mathematical and Computational Physics
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TitleBeyond Einstein : Perspectives on Geometry, Gravitation, and Cosmology in the Twentieth Century
Author(s)Rowe, David E;Sauer, Tilman;Walter, Scott A
PublicationNew York, NY, 1. Imprint: Birkh??user 2. Springer New York, 2018.
DescriptionXXIII, 492 p. 71 illus., 14 illus. in color : online resource
Abstract NoteThis volume explores the interplay between mathematical and physical research and the interactions of twentieth-century scientists within their academic communities. Beginning with Einstein???s general theory of relativity, the authors investigate a series of dramatic discoveries and rival theories in physics that influenced the development of modern differential geometry. Other sections recount the numerous methods, like the resurgence of Weyl geometry, used by geometers to solve the problems revealed by those same innovations in space-time physics. The effect of general relativity on astronomy is also addressed, namely how astronomers worked through new theories like inflationary cosmology and Phoenix models. By including recent historical research and coupling this work with many disciplines??? unique perspectives, this text provides a rich picture of general relativity and cosmology over the course of the twentieth century. The increased study on the documentation of Einstein???s early scientific work has clarified the history of science for that time and profoundly altered the way scientists view their own work, as this interdisciplinary volume demonstrates
ISBN,Price9781493977086
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. GRAVITATION 6. HISTORY 7. History of Mathematical Sciences 8. MATHEMATICS 9. Philosophy and science 10. PHILOSOPHY OF SCIENCE 11. QUANTUM PHYSICS
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TitleDifferential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields
Author(s)Rudolph, Gerd;Schmidt, Matthias
PublicationDordrecht, 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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10.    
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TitleTowards a Theory of Spacetime Theories
Author(s)Lehmkuhl, Dennis;Schiemann, Gregor;Scholz, Erhard
PublicationNew York, NY, 1. Imprint: Birkh??user 2. Springer New York, 2017.
DescriptionVIII, 335 p. 7 illus : online resource
Abstract NoteThis contributed volume is the result of a July 2010 workshop at the University of Wuppertal Interdisciplinary Centre for Science and Technology Studies which brought together world-wide experts from physics, philosophy and history, in order to address a set of questions first posed in the 1950s: How do we compare spacetime theories? How do we judge, objectively, which is the ???best??? theory? Is there even a unique answer to this question? The goal of the workshop, and of this book, is to contribute to the development of a meta-theory of spacetime theories. Such a meta-theory would reveal insights about specific spacetime theories by distilling their essential similarities and differences, deliver a framework for a class of theories that could be helpful as a blueprint to build other meta-theories, and provide a higher level viewpoint for judging which theory most accurately describes nature. But rather than drawing a map in broad strokes, the focus is on particularly rich regions in the ???space of spacetime theories.??? This work will be of interest to physicists, as well as philosophers and historians of science working with or interested in General Relativity and/or Space, Time and Gravitation more generally
ISBN,Price9781493932108
Keyword(s)1. DIFFERENTIAL GEOMETRY 2. EBOOK 3. EBOOK - SPRINGER 4. HISTORY 5. History of Mathematical Sciences 6. MATHEMATICAL PHYSICS 7. MATHEMATICS 8. Theoretical, Mathematical and Computational Physics
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