Advances In Geometry And Lie Algebras From Supergravity
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Advances In Geometry And Lie Algebras From Supergravity
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Author : Pietro Giuseppe Frè
language : en
Publisher: Springer
Release Date : 2018-02-24
Advances In Geometry And Lie Algebras From Supergravity written by Pietro Giuseppe Frè and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-24 with Science categories.
This 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.
Discrete Finite And Lie Groups
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Author : Pietro Giuseppe Fré
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-08-07
Discrete Finite And Lie Groups written by Pietro Giuseppe Fré and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-07 with Mathematics categories.
In a self contained and exhaustive work the author covers Group Theory in its multifaceted aspects, treating its conceptual foundations in a proper logical order. First discrete and finite group theory, that includes the entire chemical-physical field of crystallography is developed self consistently, followed by the structural theory of Lie Algebras with a complete exposition of the roots and Dynkin diagrams lore. A primary on Fibre-Bundles, Connections and Gauge fields, Riemannian Geometry and the theory of Homogeneous Spaces G/H is also included and systematically developed. https://petrusfremathandlit.net
Supergravity
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Author : Daniel Z. Freedman
language : en
Publisher: Cambridge University Press
Release Date : 2012-04-05
Supergravity written by Daniel Z. Freedman 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 2012-04-05 with Science categories.
Supergravity, together with string theory, is one of the most significant developments in theoretical physics. Written by two of the most respected workers in the field, this is the first-ever authoritative and systematic account of supergravity. The book starts by reviewing aspects of relativistic field theory in Minkowski spacetime. After introducing the relevant ingredients of differential geometry and gravity, some basic supergravity theories (D=4 and D=11) and the main gauge theory tools are explained. In the second half of the book, complex geometry and N=1 and N=2 supergravity theories are covered. Classical solutions and a chapter on AdS/CFT complete the book. Numerous exercises and examples make it ideal for Ph.D. students, and with applications to model building, cosmology and solutions of supergravity theories, it is also invaluable to researchers. A website hosted by the authors, featuring solutions to some exercises and additional reading material, can be found at www.cambridge.org/supergravity.
Groups And Manifolds
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Author : Pietro Giuseppe Fré
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2017-12-18
Groups And Manifolds written by Pietro Giuseppe Fré and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-18 with Science categories.
Groups and Manifolds is an introductory, yet a complete self-contained course on mathematics of symmetry: group theory and differential geometry of symmetric spaces, with a variety of examples for physicists, touching briefly also on super-symmetric field theories. The core of the course is focused on the construction of simple Lie algebras, emphasizing the double interpretation of the ADE classification as applied to finite rotation groups and to simply laced simple Lie algebras. Unique features of this book are the full-fledged treatment of the exceptional Lie algebras and a rich collection of MATHEMATICA Notebooks implementing various group theoretical constructions.
A Conceptual History Of Space And Symmetry
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Author : Pietro Giuseppe Fré
language : en
Publisher: Springer
Release Date : 2018-09-14
A Conceptual History Of Space And Symmetry written by Pietro Giuseppe Fré and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-14 with Science categories.
This book presents the author’s personal historical perspective and conceptual analysis on symmetry and geometry. The author enlightens with modern views the historical process which led to the contemporary vision of space and symmetry that are used in theoretical physics and in particular in such abstract and advanced descriptions of the physical world as those provided by supergravity. The book is written intertwining storytelling and philosophical argumentation with some essential technical material. The author argues that symmetry and geometry are inextricably entangled and their current meaning is the result of a long process of abstraction which was determined through history and can be understood within the analytic system of thought of western civilization that started with the Ancient Greeks. The evolution of geometry and symmetry theory in the last forty years has been deeply and constructively influenced by supersymmetry/supergravity and the allied constructions of strings and branes. Further advances in theoretical physics cannot be based simply on the Galilean method of interrogating nature and then formulating a testable theory to explain the observed phenomena. One ought to interrogate human thought, meaning frontier-line mathematics concerned with geometry and symmetry in order to find there the threads of so far unobserved correspondences, reinterpretations and renewed conceptions.
Recent Advances In Representation Theory Quantum Groups Algebraic Geometry And Related Topics
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Author : Pramod M. Achar
language : en
Publisher: American Mathematical Society
Release Date : 2014-08-27
Recent Advances In Representation Theory Quantum Groups Algebraic Geometry And Related Topics written by Pramod M. Achar and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-27 with Mathematics categories.
This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.
Introduction To String Theory
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Author : Sergio Cecotti
language : en
Publisher: Springer Nature
Release Date : 2023-10-06
Introduction To String Theory written by Sergio Cecotti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-06 with Science categories.
Graduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts.
Supergravity And Superstrings A Geometric Perspective In 3 Volumes
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Author : Leonardo Castellani
language : en
Publisher: World Scientific Publishing Company
Release Date : 1991-06-11
Supergravity And Superstrings A Geometric Perspective In 3 Volumes written by Leonardo Castellani and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-11 with categories.
This book provides a self-contained presentation of supergravity theories from its fundamentals to its most recent union with string and superstring theories, which are also reviewed in a self-contained manner. The subject is presented consistently in a unified geometric formalism, relying on the calculus of exterior forms and the mathematics needed to develop the theory is explained in appropriate chapters.
Recent Developments In Pseudo Riemannian Geometry
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Author : Dmitriĭ Vladimirovich Alekseevskiĭ
language : en
Publisher: European Mathematical Society
Release Date : 2008
Recent Developments In Pseudo Riemannian Geometry written by Dmitriĭ Vladimirovich Alekseevskiĭ and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are: Classification of pseudo-Riemannian symmetric spaces Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential conformal structures and conformal transformations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian manifolds Lorentzian symmetric spaces in supergravity Generalized geometries in supergravity Einstein metrics with Killing leaves The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of the art in the field as well as open problems, which can stimulate further research.
Recent Advances In Field Theory
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Author : P. Binétruy
language : en
Publisher: Elsevier
Release Date : 2016-06-03
Recent Advances In Field Theory written by P. Binétruy and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-06-03 with Science categories.
Recent Advances in Field Theory presents the proceedings of the Fourth Annecy Meeting on Theoretical Physics, held in Annecy-le-Vieux, France, on March 5–9, 1990. This book presents several relevant developments on the subject, including quantum algebra, two-dimensional quantum gravity, and topological quantum theories. Organized into 29 chapters, this book begins with an overview of the Hamiltonian quantization of the topological Chern–Simons theory. This text then examines the conformal affine Liouville model. Other chapters consider the global analyticity properties of functions correlated with causal kernels on de Sitter space. This book discusses as well the three particle models in terms of noncommutative gauge theory, namely, the Peccei-Quinn model, the Glashow–Weinberg–Salam model, and the standard model. The final chapter deals with the development on the construction of lattice integrable models corresponding to the SU (N) coset conformal field theories. This book is a valuable resource for physicists and scientists.