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 Science 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.
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.
Supersymmetry In Mathematics And Physics
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Author : Sergio Ferrara
language : en
Publisher: Springer
Release Date : 2011-08-27
Supersymmetry In Mathematics And Physics written by Sergio Ferrara and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-27 with Mathematics categories.
Supersymmetry was created by the physicists in the 1970's to give a unified treatment of fermions and bosons, the basic constituents of matter. Since then its mathematical structure has been recognized as that of a new development in geometry, and mathematicians have busied themselves with exploring this aspect. This volume collects recent advances in this field, both from a physical and a mathematical point of view, with an accent on a rigorous treatment of the various questions raised.
Discrete Finite And Lie Groups
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Author : Pietro Giuseppe Fré
language : en
Publisher:
Release Date : 2023-09-18
Discrete Finite And Lie Groups written by Pietro Giuseppe Fré and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-18 with 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.
Supergravity And Superstrings A Geometric Perspective In 3 Volumes
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Author : Castellani Leonardo
language : en
Publisher: World Scientific Publishing Company
Release Date : 1991-06-11
Supergravity And Superstrings A Geometric Perspective In 3 Volumes written by Castellani Leonardo 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.
New Developments In Lie Theory And Geometry
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Author : Carolyn Gordon
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
New Developments In Lie Theory And Geometry written by Carolyn Gordon 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 2009 with Geometry, Differential categories.
This volume is an outgrowth of the Sixth Workshop on Lie Theory and Geometry, held in the province of Cordoba, Argentina in November 2007. The representation theory and structure theory of Lie groups play a pervasive role throughout mathematics and physics. Lie groups are tightly intertwined with geometry and each stimulates developments in the other. The aim of this volume is to bring to a larger audience the mutually beneficial interaction between Lie theorists and geometers that animated the workshop. Two prominent themes of the representation theoretic articles are Gelfand pairs and the representation theory of real reductive Lie groups. Among the more geometric articles are an exposition of major recent developments on noncompact homogeneous Einstein manifolds and aspects of inverse spectral geometry presented in settings accessible to readers new to the area.
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.
An Introduction To Lie Groups And The Geometry Of Homogeneous Spaces
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Author : Andreas Arvanitogeōrgos
language : en
Publisher: American Mathematical Soc.
Release Date : 2003-01-01
An Introduction To Lie Groups And The Geometry Of Homogeneous Spaces written by Andreas Arvanitogeōrgos 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 2003-01-01 with Mathematics categories.
It is remarkable that so much about Lie groups could be packed into this small book. But after reading it, students will be well-prepared to continue with more advanced, graduate-level topics in differential geometry or the theory of Lie groups. The theory of Lie groups involves many areas of mathematics: algebra, differential geometry, algebraic geometry, analysis, and differential equations. In this book, Arvanitoyeorgos outlines enough of the prerequisites to get the readerstarted. He then chooses a path through this rich and diverse theory that aims for an understanding of the geometry of Lie groups and homogeneous spaces. In this way, he avoids the extra detail needed for a thorough discussion of representation theory. Lie groups and homogeneous spaces are especiallyuseful to study in geometry, as they provide excellent examples where quantities (such as curvature) are easier to compute. A good understanding of them provides lasting intuition, especially in differential geometry. The author provides several examples and computations. Topics discussed include the classification of compact and connected Lie groups, Lie algebras, geometrical aspects of compact Lie groups and reductive homogeneous spaces, and important classes of homogeneous spaces, such assymmetric spaces and flag manifolds. Applications to more advanced topics are also included, such as homogeneous Einstein metrics, Hamiltonian systems, and homogeneous geodesics in homogeneous spaces. The book is suitable for advanced undergraduates, graduate students, and research mathematiciansinterested in differential geometry and neighboring fields, such as topology, harmonic analysis, and mathematical physics.
Introduction To String Theory
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Author : Sergio Cecotti
language : en
Publisher: Springer Nature
Release Date : 2023-11-07
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 2023-11-07 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.