Categories In Algebra Geometry And Mathematical Physics
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Differential Geometry And Mathematical Physics
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Author : Gerd Rudolph
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-09
Differential Geometry And Mathematical Physics written by Gerd Rudolph and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-09 with Science categories.
Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.
Lie Groups And Algebras With Applications To Physics Geometry And Mechanics
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Author : D.H. Sattinger
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Lie Groups And Algebras With Applications To Physics Geometry And Mechanics written by D.H. Sattinger and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Mathematics categories.
This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselvesto the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.
A Course In Modern Mathematical Physics
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Author : Peter Szekeres
language : en
Publisher: Cambridge University Press
Release Date : 2004-12-16
A Course In Modern Mathematical Physics written by Peter Szekeres and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-16 with Mathematics categories.
This textbook, first published in 2004, provides an introduction to the major mathematical structures used in physics today.
Categories In Algebra Geometry And Mathematical Physics
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Author : Alexei Davydov
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Categories In Algebra Geometry And Mathematical Physics written by Alexei Davydov and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Category theory has become the universal language of modern mathematics. This book is a collection of articles applying methods of category theory to the areas of algebra, geometry, and mathematical physics. Among others, this book contains articles on higher categories and their applications and on homotopy theoretic methods. The reader can learn about the exciting new interactions of category theory with very traditional mathematical disciplines.
Category Theory In Physics Mathematics And Philosophy
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Author : Marek Kuś
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Category Theory In Physics Mathematics And Philosophy written by Marek Kuś and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Science categories.
The contributions gathered here demonstrate how categorical ontology can provide a basis for linking three important basic sciences: mathematics, physics, and philosophy. Category theory is a new formal ontology that shifts the main focus from objects to processes. The book approaches formal ontology in the original sense put forward by the philosopher Edmund Husserl, namely as a science that deals with entities that can be exemplified in all spheres and domains of reality. It is a dynamic, processual, and non-substantial ontology in which all entities can be treated as transformations, and in which objects are merely the sources and aims of these transformations. Thus, in a rather surprising way, when employed as a formal ontology, category theory can unite seemingly disparate disciplines in contemporary science and the humanities, such as physics, mathematics and philosophy, but also computer and complex systems science.
Mal Cev Protomodular Homological And Semi Abelian Categories
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Author : Francis Borceux
language : en
Publisher: Springer Science & Business Media
Release Date : 2004-02-29
Mal Cev Protomodular Homological And Semi Abelian Categories written by Francis Borceux and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-29 with Mathematics categories.
The purpose of the book is to take stock of the situation concerning Algebra via Category Theory in the last fifteen years, where the new and synthetic notions of Mal'cev, protomodular, homological and semi-abelian categories emerged. These notions force attention on the fibration of points and allow a unified treatment of the main algebraic: homological lemmas, Noether isomorphisms, commutator theory. The book gives full importance to examples and makes strong connections with Universal Algebra. One of its aims is to allow appreciating how productive the essential categorical constraint is: knowing an object, not from inside via its elements, but from outside via its relations with its environment. The book is intended to be a powerful tool in the hands of researchers in category theory, homology theory and universal algebra, as well as a textbook for graduate courses on these topics.
Higher Operads Higher Categories
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Author : Tom Leinster
language : en
Publisher: Cambridge University Press
Release Date : 2004-07-22
Higher Operads Higher Categories written by Tom Leinster and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-07-22 with Mathematics categories.
Foundations of higher dimensional category theory for graduate students and researchers in mathematics and mathematical physics.
Kac Moody Groups Their Flag Varieties And Representation Theory
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Author : Shrawan Kumar
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-09-10
Kac Moody Groups Their Flag Varieties And Representation Theory written by Shrawan Kumar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-09-10 with Mathematics categories.
"Most of these topics appear here for the first time in book form. Many of them are interesting even in the classical case of semi-simple algebraic groups. Some appendices recall useful results from other areas, so the work may be considered self-contained, although some familiarity with semi-simple Lie algebras or algebraic groups is helpful. It is clear that this book is a valuable reference for all those interested in flag varieties and representation theory in the semi-simple or Kac-Moody case." —MATHEMATICAL REVIEWS "A lot of different topics are treated in this monumental work. . . . many of the topics of the book will be useful for those only interested in the finite-dimensional case. The book is self contained, but is on the level of advanced graduate students. . . . For the motivated reader who is willing to spend considerable time on the material, the book can be a gold mine. " —ZENTRALBLATT MATH
Special Matrices Of Mathematical Physics
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Author : Ruben Aldrovandi
language : en
Publisher: World Scientific
Release Date : 2001
Special Matrices Of Mathematical Physics written by Ruben Aldrovandi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Ch. 1. Some fundamental notions. 1.1. Definitions. 1.2. Components of a matrix. 1.3. Matrix functions. 1.4. Normal matrices -- ch. 2. Evolving systems -- ch. 3. Markov chains. 3.1. Non-negative matrices. 3.2. General properties -- ch. 4. Glass transition -- ch. 5. The Kerner model. 5.1. A simple example: Se-As glass -- ch. 6. Formal developments. 6.1. Spectral aspects. 6.2. Reducibility and regularity. 6.3. Projectors and asymptotics. 6.4. Continuum time -- ch. 7. Equilibrium, dissipation and ergodicity. 7.1. Recurrence, transience and periodicity. 7.2. Detailed balancing and reversibility. 7.3. Ergodicity -- ch. 8. Prelude -- ch. 9. Definition and main properties. 9.1. Bases. 9.2. Double Fourier transform. 9.3. Random walks -- ch. 10. Discrete quantum mechanics. 10.1. Introduction. 10.2. Weyl-Heisenberg groups. 10.3. Weyl-Wigner transformations. 10.4. Braiding and quantum groups -- ch. 11. Quantum symplectic structure. 11.1. Matrix differential geometry. 11.2. The symplectic form. 11.3. The quantum fabric -- ch. 12. An organizing tool -- ch. 13. Bell polynomials. 13.1. Definition and elementary properties. 13.2. The matrix representation. 13.3. The Lagrange inversion formula. 13.4. Developments -- ch. 14. Determinants and traces. 14.1. Introduction. 14.2. Symmetric functions. 14.3. Polynomials. 14.4. Characteristic polynomials. 14.5. Lie algebras invariants -- ch. 15. Projectors and iterates. 15.1. Projectors, revisited. 15.2. Continuous iterates -- ch. 16. Gases: real and ideal. 16.1. Microcanonical ensemble. 16.2. The canonical ensemble. 16.3. The grand canonical ensemble. 16.4. Braid statistics. 16.5. Condensation theories. 16.6. The Fredholm formalism.
New Foundations In Mathematics
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Author : Garret Sobczyk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-10-28
New Foundations In Mathematics written by Garret Sobczyk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-28 with Mathematics categories.
The first book of its kind, New Foundations in Mathematics: The Geometric Concept of Number uses geometric algebra to present an innovative approach to elementary and advanced mathematics. Geometric algebra offers a simple and robust means of expressing a wide range of ideas in mathematics, physics, and engineering. In particular, geometric algebra extends the real number system to include the concept of direction, which underpins much of modern mathematics and physics. Much of the material presented has been developed from undergraduate courses taught by the author over the years in linear algebra, theory of numbers, advanced calculus and vector calculus, numerical analysis, modern abstract algebra, and differential geometry. The principal aim of this book is to present these ideas in a freshly coherent and accessible manner. New Foundations in Mathematics will be of interest to undergraduate and graduate students of mathematics and physics who are looking for a unified treatment of many important geometric ideas arising in these subjects at all levels. The material can also serve as a supplemental textbook in some or all of the areas mentioned above and as a reference book for professionals who apply mathematics to engineering and computational areas of mathematics and physics.