Author: Pietro Fre
Publisher: World Scientific
ISBN: 9814501360
Category : Science
Languages : en
Pages : 484
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Book Description
This book presents, in a unifying perspective, the topics related to N=2 supersymmetry in two dimensions. Beginning with the Kähler structure of D=4 supergravity Lagrangians, through the analysis of string compactifications on Calabi-Yau manifolds, one reaches the heart of the matter with the chiral ring structure of N=2 conformal field theories and its relation to topological field theory models and Landau-Ginzburg models. In addition, mirror symmetry, topological twists and Picard-Fuchs equations are discussed.
Author: P. Fr
Publisher: World Scientific
ISBN: 9789810220273
Category : Science
Languages : en
Pages : 486
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Book Description
This book presents, in a unifying perspective, the topics related to N=2 supersymmetry in two dimensions. Beginning with the Khler structure of D=4 supergravity Lagrangians, through the analysis of string compactifications on Calabi-Yau manifolds, one reaches the heart of the matter with the chiral ring structure of N=2 conformal field theories and its relation to topological field theory models and Landau-Ginzburg models. In addition, mirror symmetry, topological twists and Picard-Fuchs equations are discussed.
Author: Stefano Marchiafava
Publisher: World Scientific
ISBN: 981281003X
Category : Mathematics
Languages : en
Pages : 486
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Book Description
During the last five years, after the first meeting on OC Quaternionic Structures in Mathematics and PhysicsOCO, interest in quaternionic geometry and its applications has continued to increase. Progress has been made in constructing new classes of manifolds with quaternionic structures (quaternionic Knhler, hyper-Knhler, hyper-complex, etc.), studying the differential geometry of special classes of such manifolds and their submanifolds, understanding relations between the quaternionic structure and other differential-geometric structures, and also in physical applications of quaternionic geometry. Some generalizations of classical quaternion-like structures (like HKT structures and hyper-Knhler manifolds with singularities) appeared naturally and were studied. Some of those results are published in this book. Contents: Hypercomplex Structures on Special Classes of Nilpotent and Solvable Lie Groups (M L Barberis); Twistor Quotients of HyperKnhler Manifolds (R Bielawski); Quaternionic Contact Structures (O Biquard); A New Construction of Homogeneous Quaternionic Manifolds and Related Geometric Structures (V Cortes); Quaternion Knhler Flat Manifolds (I G Dotti); A Canonical HyperKnhler Metric on the Total Space of a Cotangent Bundle (D Kaledin); Special Spinors and Contact Geometry (A Moroianu); Brane Solitons and Hypercomplex Structures (G Papadopoulos); Hypercomplex Geometry (H Pedersen); Examples of HyperKnhler Connections with Torsion (Y S Poon); A New Weight System on Chord Diagrams via HyperKnhler Geometry (J Sawon); Vanishing Theorems for Quaternionic Knhler Manifolds (U Semmelmann & G Weingart); Weakening Holonomy (A Swann); Special Knhler Geometry (A Van Proeyen); Singularities in HyperKnhler Geometry (M Verbitsky); and other papers. Readership: Researchers and graduate students in geometry, topology, mathematical physics and theoretical physics."
Author: Arthur Hebecker
Publisher: Springer Nature
ISBN: 3030651517
Category : Science
Languages : en
Pages : 321
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Book Description
This book presents a string-theoretic approach to new ideas in particle physics, also known as Physics Beyond the Standard Model, and to cosmology. The concept of Naturalness and its apparent violation by the low electroweak scale and the small cosmological constant is emphasized. It is shown that string theory, through its multitude of solutions, known as the landscape, offers a partial resolution to these naturalness problems as well as suggesting more speculative possibilities like that of a multiverse. The book is based on a one-semester course, as such, it has a pedagogical approach, is self-contained and includes many exercises with solutions. Notably, the basics of string theory are introduced as part of the lectures. These notes are aimed at graduate students with a solid background in quantum field theory, as well as at young researchers from theoretical particle physics to mathematical physics. This text also benefits students who are in the process of studying string theory at a deeper level. In this case, the volume serves as additional reading beyond a formal string theory course.
Author: Edoardo Lauria
Publisher: Springer Nature
ISBN: 303033757X
Category : Science
Languages : en
Pages : 265
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Book Description
This graduate-level primer presents a tutorial introduction to and overview of N = 2 supergravity theories - with 8 real supercharges and in 4, 5 and 6 dimensions. First, the construction of such theories by superconformal methods is explained in detail, and relevant special geometries are obtained and characterized. Following, the relation between the supergravity theories in the various dimensions is discussed. This leads eventually to the concept of very special geometry and quaternionic-Kähler manifolds. This concise text is a valuable resource for graduate students and young researchers wishing to enter the field quickly and efficiently.
Author: Gava E
Publisher: World Scientific
ISBN: 9814547735
Category :
Languages : en
Pages : 728
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Book Description
Author: Eberhard Zeidler
Publisher: Springer Science & Business Media
ISBN: 3642224210
Category : Mathematics
Languages : en
Pages : 1141
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Book Description
In this third volume of his modern introduction to quantum field theory, Eberhard Zeidler examines the mathematical and physical aspects of gauge theory as a principle tool for describing the four fundamental forces which act in the universe: gravitative, electromagnetic, weak interaction and strong interaction. Volume III concentrates on the classical aspects of gauge theory, describing the four fundamental forces by the curvature of appropriate fiber bundles. This must be supplemented by the crucial, but elusive quantization procedure. The book is arranged in four sections, devoted to realizing the universal principle force equals curvature: Part I: The Euclidean Manifold as a Paradigm Part II: Ariadne's Thread in Gauge Theory Part III: Einstein's Theory of Special Relativity Part IV: Ariadne's Thread in Cohomology For students of mathematics the book is designed to demonstrate that detailed knowledge of the physical background helps to reveal interesting interrelationships among diverse mathematical topics. Physics students will be exposed to a fairly advanced mathematics, beyond the level covered in the typical physics curriculum. Quantum Field Theory builds a bridge between mathematicians and physicists, based on challenging questions about the fundamental forces in the universe (macrocosmos), and in the world of elementary particles (microcosmos).
Author: Eberhard Zeidler
Publisher: Springer Science & Business Media
ISBN: 354034764X
Category : Science
Languages : en
Pages : 1060
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Book Description
This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.
Author: Sergio M. Kuzenko
Publisher: CRC Press
ISBN: 1420050516
Category : Science
Languages : en
Pages : 677
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Book Description
Ideas and Methods of Supersymmetry and Supergravity: Or a Walk Through Superspace provides a comprehensive, detailed, and self-contained account of four dimensional simple supersymmetry and supergravity. Throughout the book, the authors cultivate their material in detail with calculations and full discussions of the fundamental ideas and motivations. They develop the subject in its superfield formulations but where appropriate for illustration, analogy, and comparison with conventional field theory, they use the component formulation. The book discusses many subjects that, until now, can only be found in the research literature. In addition, it presents a plethora of new results. Combining classical and quantum field theory with group theory, differential geometry, and algebra, the book begins with a solid mathematical background that is used in the rest of the book. The next chapter covers algebraic aspects of supersymmetry and the concepts of superspace and superfield. In the following chapters, the book presents classical and quantum superfield theory and the superfield formulation of supergravity. A synthesis of results and methods developed in the book, the final chapter concludes with the theory of effective action in curved superspaces. After studying this book, readers should be well prepared to pursue independent research in any area of supersymmetry and supergravity. It will be an indispensable source of reference for advanced graduate students, postdoctoral faculty, and researchers involved in quantum field theory, high energy physics, gravity theory, mathematical physics, and applied mathematics.
Author: Pietro Giuseppe Frè
Publisher: Springer Science & Business Media
ISBN: 9400754434
Category : Science
Languages : en
Pages : 466
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Book Description
‘Gravity, a Geometrical Course’ presents general relativity (GR) in a systematic and exhaustive way, covering three aspects that are homogenized into a single texture: i) the mathematical, geometrical foundations, exposed in a self consistent contemporary formalism, ii) the main physical, astrophysical and cosmological applications, updated to the issues of contemporary research and observations, with glimpses on supergravity and superstring theory, iii) the historical development of scientific ideas underlying both the birth of general relativity and its subsequent evolution. The book is divided in two volumes. Volume Two is covers black holes, cosmology and an introduction to supergravity. The aim of this volume is two-fold. It completes the presentation of GR and it introduces the reader to theory of gravitation beyond GR, which is supergravity. Starting with a short history of the black hole concept, the book covers the Kruskal extension of the Schwarzschild metric, the causal structures of Lorentzian manifolds, Penrose diagrams and a detailed analysis of the Kerr-Newman metric. An extensive historical account of the development of modern cosmology is followed by a detailed presentation of its mathematical structure, including non-isotropic cosmologies and billiards, de Sitter space and inflationary scenarios, perturbation theory and anisotropies of the Cosmic Microwave Background. The last three chapters deal with the mathematical and conceptual foundations of supergravity in the frame of free differential algebras. Branes are presented both as classical solutions of the bulk theory and as world-volume gauge theories with particular emphasis on the geometrical interpretation of kappa-supersymmetry. The rich bestiary of special geometries underlying supergravity lagrangians is presented, followed by a chapter providing glances on the equally rich collection of special solutions of supergravity. Pietro Frè is Professor of Theoretical Physics at the University of Torino, Italy and is currently serving as Scientific Counsellor of the Italian Embassy in Moscow. His scientific passion lies in supergravity and all allied topics, since the inception of the field, in 1976. He was professor at SISSA, worked in the USA and at CERN. He has taught General Relativity for 15 years. He has previously two scientific monographs, “Supergravity and Superstrings” and “The N=2 Wonderland”, He is also the author of a popular science book on cosmology and two novels, in Italian.
