Supergeometry Super Riemann Surfaces And The Superconformal Action Functional

Author : Enno Keßler
Publisher : Springer Nature
Page : 305 pages
File Size : 54,5 Mb
Release : 2019-08-28
Category : Mathematics
ISBN : 9783030137588

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Supergeometry, Super Riemann Surfaces and the Superconformal Action Functional by Enno Keßler Pdf

This book treats the two-dimensional non-linear supersymmetric sigma model or spinning string from the perspective of supergeometry. The objective is to understand its symmetries as geometric properties of super Riemann surfaces, which are particular complex super manifolds of dimension 1|1. The first part gives an introduction to the super differential geometry of families of super manifolds. Appropriate generalizations of principal bundles, smooth families of complex manifolds and integration theory are developed. The second part studies uniformization, U(1)-structures and connections on Super Riemann surfaces and shows how the latter can be viewed as extensions of Riemann surfaces by a gravitino field. A natural geometric action functional on super Riemann surfaces is shown to reproduce the action functional of the non-linear supersymmetric sigma model using a component field formalism. The conserved currents of this action can be identified as infinitesimal deformations of the super Riemann surface. This is in surprising analogy to the theory of Riemann surfaces and the harmonic action functional on them. This volume is aimed at both theoretical physicists interested in a careful treatment of the subject and mathematicians who want to become acquainted with the potential applications of this beautiful theory.

Author : Felix Finster,Johannes Kleiner,Christian Röken,Jürgen Tolksdorf
Publisher : Birkhäuser
Page : 518 pages
File Size : 42,6 Mb
Release : 2016-02-24
Category : Science
ISBN : 9783319269023

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Quantum Mathematical Physics by Felix Finster,Johannes Kleiner,Christian Röken,Jürgen Tolksdorf Pdf

Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.

Author : Katrina Barron
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 42,6 Mb
Release : 2003
Category : Infinite dimensional Lie algebras
ISBN : 9780821832608

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The Moduli Space of $N=1$ Superspheres with Tubes and the Sewing Operation by Katrina Barron Pdf

Within the framework of complex supergeometry and motivated by two-dimensional genus-zero holomorphic $N = 1$ superconformal field theory, this book defines the moduli space of $N=1$ genus-zero super-Riemann surfaces with oriented and ordered half-infinite tubes, modulo superconformal equivalence.

Author : Pati Jogesh C,Randjbar-daemi Seifallah,Sezgin Ergin
Publisher : World Scientific
Page : 708 pages
File Size : 51,7 Mb
Release : 1990-05-01
Category : Electronic
ISBN : 9789814611756

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High Energy Physics And Cosmology - 1989 Summer School by Pati Jogesh C,Randjbar-daemi Seifallah,Sezgin Ergin Pdf

Author : Alice Rogers
Publisher : World Scientific
Page : 262 pages
File Size : 47,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812708854

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Supermanifolds by Alice Rogers Pdf

This book aims to fill the gap in the available literature on supermanifolds, describing the different approaches to supermanifolds together with various applications to physics, including some which rely on the more mathematical aspects of supermanifold theory. The first part of the book contains a full introduction to the theory of supermanifolds, comparing and contrasting the different approaches that exist. Topics covered include tensors on supermanifolds, super fibre bundles, super Lie groups and integration theory. Later chapters emphasise applications, including the superspace approach to supersymmetric theories, super Riemann surfaces and the spinning string, path integration on supermanifolds and BRST quantization.

Author : Jürgen Jost
Publisher : Springer Science & Business Media
Page : 226 pages
File Size : 44,8 Mb
Release : 2009-08-17
Category : Mathematics
ISBN : 9783642005411

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Geometry and Physics by Jürgen Jost Pdf

"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.

Author : Anonim
Publisher : Unknown
Page : 724 pages
File Size : 54,5 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015026169683

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Mathematical Reviews by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 624 pages
File Size : 41,7 Mb
Release : 1994
Category : Particles (Nuclear physics)
ISBN : PSU:000052636387

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High Energy Physics Index by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 1454 pages
File Size : 40,8 Mb
Release : 1991
Category : Physics
ISBN : STANFORD:36105000902960

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Physics Briefs by Anonim Pdf

Author : Daniel S. Freed
Publisher : American Mathematical Soc.
Page : 186 pages
File Size : 50,8 Mb
Release : 2019-08-23
Category : Algebraic topology
ISBN : 9781470452063

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Lectures on Field Theory and Topology by Daniel S. Freed Pdf

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.

Author : Matti Pitkanen
Publisher : Bentham Science Publishers
Page : 1235 pages
File Size : 47,6 Mb
Release : 2016-03-03
Category : Science
ISBN : 9781681081793

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Topological Geometrodynamics by Matti Pitkanen Pdf

Topological geometrodynamics (TGD) is a modification of the theory of general relativity inspired by the problems related to the definition of inertial and gravitational energies in the earlier hypotheses. TGD is also a generalization of super string models. TGD brings forth an elegant theoretical projection of reality and builds upon the work by renowned scientists (Wheeler, Feynman, Penrose, Einstein, Josephson to name a few). In TGD, Physical space-time planes are visualized as four-dimensional surfaces in a certain 8-dimensional space (H). The choice of H is fixed by symmetries of standard model and leads to a geometric mapping of known classical fields and elementary particle numbers. TGD differs from Einstein’s geometrodynamics in the way space-time planes or ‘sheets’ are lumped together. Extending the theory based on fusing number concepts implies a further generalisation of the space-time concept allowing the identification of space-time correlates of cognition and intentionality. Additionally, zero energy ontology forces an extension of quantum measurement theory to a theory of consciousness and a hierarchy of phases is identified. Dark matter is thus predicted with far reaching implications for the understanding of consciousness and living systems. Therefore, it sets a solid foundation for modeling our universe in geometric terms. Topological Geometrodynamics: An Overview explains basic and advanced concepts about TGD. The book covers introductory information and classical TGD concepts before delving into twistor-space theory, particle physics, infinite-dimensional spinor geometry, generalized number theory, Planck constants, and the applications of TGD theory in research. The book is a valuable guide to TDG theory for researchers and advanced graduates in theoretical physics and cosmology.

Author : Peter C. West
Publisher : World Scientific
Page : 448 pages
File Size : 48,7 Mb
Release : 1990
Category : Science
ISBN : 9810200994

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Introduction to Supersymmetry and Supergravity by Peter C. West Pdf

To the 1st edition of this monograph (addressed to advanced graduate students and researchers ) the author, responding to developments within superstring theory, has added 51/2 chapters dealing with two- dimensional supersymmetry. Authoritative, as lucid as the subject matter allows (yet demanding nonetheless!), attractively produced and priced. (NW) Annotation copyrighted by Book News, Inc., Portland, OR

Author : Raymond O. Wells
Publisher : Springer Science & Business Media
Page : 315 pages
File Size : 52,5 Mb
Release : 2007-10-31
Category : Mathematics
ISBN : 9780387738918

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Differential Analysis on Complex Manifolds by Raymond O. Wells Pdf

A brand new appendix by Oscar Garcia-Prada graces this third edition of a classic work. In developing the tools necessary for the study of complex manifolds, this comprehensive, well-organized treatment presents in its opening chapters a detailed survey of recent progress in four areas: geometry (manifolds with vector bundles), algebraic topology, differential geometry, and partial differential equations. Wells’s superb analysis also gives details of the Hodge-Riemann bilinear relations on Kahler manifolds, Griffiths's period mapping, quadratic transformations, and Kodaira's vanishing and embedding theorems. Oscar Garcia-Prada’s appendix gives an overview of the developments in the field during the decades since the book appeared.

Author : Sergio Ferrara,Rita Fioresi,V.S. Varadarajan
Publisher : Springer
Page : 279 pages
File Size : 52,6 Mb
Release : 2011-08-27
Category : Mathematics
ISBN : 9783642217449

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Supersymmetry in Mathematics and Physics by Sergio Ferrara,Rita Fioresi,V.S. Varadarajan Pdf

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.

Author : Valery A. Gritsenko,Vyacheslav P. Spiridonov
Publisher : Springer Nature
Page : 422 pages
File Size : 40,7 Mb
Release : 2020-07-09
Category : Mathematics
ISBN : 9783030424008

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Partition Functions and Automorphic Forms by Valery A. Gritsenko,Vyacheslav P. Spiridonov Pdf

This book offers an introduction to the research in several recently discovered and actively developing mathematical and mathematical physics areas. It focuses on: 1) Feynman integrals and modular functions, 2) hyperbolic and Lorentzian Kac-Moody algebras, related automorphic forms and applications to quantum gravity, 3) superconformal indices and elliptic hypergeometric integrals, related instanton partition functions, 4) moonshine, its arithmetic aspects, Jacobi forms, elliptic genus, and string theory, and 5) theory and applications of the elliptic Painleve equation, and aspects of Painleve equations in quantum field theories. All the topics covered are related to various partition functions emerging in different supersymmetric and ordinary quantum field theories in curved space-times of different (d=2,3,...,6) dimensions. Presenting multidisciplinary methods (localization, Borcherds products, theory of special functions, Cremona maps, etc) for treating a range of partition functions, the book is intended for graduate students and young postdocs interested in the interaction between quantum field theory and mathematics related to automorphic forms, representation theory, number theory and geometry, and mirror symmetry.