Manifolds Groups Bundles And Spacetime

Author : R. Dale Gray
Publisher : Lulu.com
Page : 420 pages
File Size : 41,8 Mb
Release : 2015-08-27
Category : Science
ISBN : 9781329408258

Get Book

Manifolds, Groups, Bundles, and Spacetime by R. Dale Gray Pdf

Manifolds, Groups, Bundles, and Spacetime was written for those who are interested in modern differential geometry and its applications in physics. The primary material is suitable for a graduate level course in the theory of differentiable manifolds, Lie groups, and fiber bundles. The first two chapters are an introduction to concepts from linear algebra and tensors and can be read to establish familiarity with the notation and conventions of the text by those who are already familiar with these topics. The third and fourth chapters are a review of topics from advanced calculus and topology and are included primarily as a convenient reference.

Author : J. Hano,H. Ozeki,K. Okamoto,S. Murakami,A. Morimoto
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 53,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9781461259879

Get Book

Manifolds and Lie Groups by J. Hano,H. Ozeki,K. Okamoto,S. Murakami,A. Morimoto Pdf

This volume is the collection of papers dedicated to Yozo Matsushima on his 60th birthday, which took place on February 11, 1980. A conference in Geometry in honor of Professor Matsushima was held at the University of Notre Dame on May 14 and 15, 1980. Some of the papers in this volume were delivered on this occasion. 0 00 0\ - 15 S. Kobayashi, University 27 R. Ogawa, Loyola 42 P. Ryan, Indiana 1 W. Stoll 2 W. Kaup, University of of California at Berkeley University (Chicago) University at South Bend Tubing en 16 B.Y. Chen, 28 A. Howard 43 M. Kuga, SUNY at 3 G. Shimura, Michigan State University 29 D. Blair, Stony Brook Princeton University 17 G. Ludden, Michigan State University 44 W. Higgins 30 B. Smyth 4 A. Borel, Institute for Michigan State University 45 J. Curry Advanced Study 18 S. Harris, 31 A. Pradhan 46 D. Norris 32 R. Escobales, 5 Y. Matsushima University of Missouri 47 J. Spellecy Canisius College 6 Mrs. Matsushima 19 J. Beem, 48 M. Clancy 7 K. Nomizu, University of Missouri 33 L. Smiley 49 J. Rabinowitz, University 20 D. Collins, 34 C.H. Sung Brown University of Illinois at Chicago Valparaiso University 35 M. Markowitz 8 J.-1. Hano, 50 R. Richardson, Australian Washington University 36 A. Sommese 21 I. Satake, University of National University California at Berkeley 37 A. Vitter, 9 J. Carrell, University of 51 D. Lieberman, 22 H.

Author : C. T. J. Dodson
Publisher : Unknown
Page : 244 pages
File Size : 49,6 Mb
Release : 1980
Category : Mathematics
ISBN : UOM:39076006533298

Get Book

Categories, Bundles, and Spacetime Topology by C. T. J. Dodson Pdf

Author : Heinrich Saller
Publisher : Springer
Page : 574 pages
File Size : 53,7 Mb
Release : 2017-06-19
Category : Science
ISBN : 9783319586649

Get Book

Operational Symmetries by Heinrich Saller Pdf

This book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space. The spectrum of hyperbolic position space explains the properties of the nonrelativistic atoms; the spectrum of electroweak spacetime is hoped to explain those of the basic interactions and elementary particles. In this book, the theory of operational symmetries is developed from the numbers, from Plato’s and Kepler’s symmetries over the simple Lie groups to their applications in nonrelativistic, special relativistic and general relativistic quantum theories with the atomic spectrum for hyperbolic position and, in first attempts, the particle spectrum for electroweak spacetime. The standard model of elementary particles and interactions is characterized by a symmetry group. In general, as initiated by Weyl and stressed by Heisenberg, quantum theory can be built as a theory of operation groups and their unitary representations. In such a framework, time, position and spacetime is modeled by equivalence classes of symmetry groups. For a unification on this road, the quest is not for a final theory with a basic equation for basic particles, but for the basic operation group and its representations.

Author : Robert Wasserman
Publisher : Oxford University Press, USA
Page : 409 pages
File Size : 53,8 Mb
Release : 1992
Category : Science
ISBN : 0195065611

Get Book

Tensors and Manifolds by Robert Wasserman Pdf

This book is based on courses taken by advanced undergraduate and beginning graduate students in mathematics and physics at Michigan State University. The courses were intended to present an introduction to the expanse of modern mathematics and its applications in modern mathematics and its application in modern physics. This book gives an introduction perspective to young students intending to go into a field of pure mathematics, and who, with the usual 'pigeon-hold' graduate curriculum, will not get an overall perspective for several years, much less any idea of application.

Author : C.T. Dodson
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 49,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401577762

Get Book

Categories, Bundles and Spacetime Topology by C.T. Dodson Pdf

Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Gad in Crane Feathers' in R. Brown'The point of a Pin'. van Gulik's TheChinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging SUbdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Author : Steinar Johannesen
Publisher : Chapman & Hall/CRC
Page : 0 pages
File Size : 44,7 Mb
Release : 2017
Category : Differential equations
ISBN : 1498796710

Get Book

Smooth Manifolds and Fibre Bundles with Applications to Theoretical Physics by Steinar Johannesen Pdf

Covariant derivative of forms on principal bundles -- The curvature form -- Horizontal lifts of vector fields -- Local sections and trivializations -- Horizontal lifts of curves -- Parallel transport -- Forms in associated bundles -- Covariant derivative of sections in associated vector bundles -- Covariant derivative of tensor fields -- Covariant derivative of sections along smooth maps -- Linear connections -- Koszul connections -- Structure equations -- Geodesics -- Metrical connections -- The Schwarzschild - de Sitter spacetime -- Affine transformations and Killing vector fields -- Conformal transformations -- 11 ISOMETRIC IMMERSIONS AND THE SECOND FUNDAMENTAL FORM -- Connections in reduced subbundles -- The normal bundle and the bundle of adapted orthonormal frames -- The second fundamental form -- The shape tensor -- The shape operator -- The formulae of Gauss and Weingarten -- Strain and vorticity -- The equations of Gauss, Ricci and Codazzi -- Pseudo-Riemannian hypersurfaces -- The Robertson-Walker spacetime -- The Friedmann cosmological models -- 12 JET BUNDLES -- Bundles -- Affine bundles -- Derivations and the Frölicher-Nijenhuis bracket -- First order jet bundles -- Holonomic tangent vectors -- Contact cotangent vectors -- Jet fields and connections -- Equivariant jet fields -- Second order jet bundles -- Prolongation of vector fields -- Calculus of variations -- A: PRELIMINARIES -- Maps -- The permutation group -- Group actions -- Categories and functors -- Connectivity -- Homotopy theory -- Coverings -- Topological groups -- Topological vector spaces -- Bibliography -- Index

Author : Robert Wasserman
Publisher : Oxford University Press, USA
Page : 468 pages
File Size : 47,6 Mb
Release : 2004
Category : Language Arts & Disciplines
ISBN : 0198510594

Get Book

Tensors and Manifolds by Robert Wasserman Pdf

This book sets forth the basic principles of tensors and manifolds and describes how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics.

Author : Yvonne Choquet-Bruhat,Cécile DeWitt-Morette,Margaret Dillard-Bleick
Publisher : Gulf Professional Publishing
Page : 666 pages
File Size : 52,5 Mb
Release : 1982
Category : Mathematics
ISBN : 0444860177

Get Book

Analysis, Manifolds and Physics Revised Edition by Yvonne Choquet-Bruhat,Cécile DeWitt-Morette,Margaret Dillard-Bleick Pdf

This reference book, which has found wide use as a text, provides an answer to the needs of graduate physical mathematics students and their teachers. The present edition is a thorough revision of the first, including a new chapter entitled ``Connections on Principle Fibre Bundles'' which includes sections on holonomy, characteristic classes, invariant curvature integrals and problems on the geometry of gauge fields, monopoles, instantons, spin structure and spin connections. Many paragraphs have been rewritten, and examples and exercises added to ease the study of several chapters. The index includes over 130 entries.

Author : Pietro Giuseppe Fré,Alexander Fedotov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 496 pages
File Size : 45,6 Mb
Release : 2017-12-18
Category : Science
ISBN : 9783110551204

Get Book

Groups and Manifolds by Pietro Giuseppe Fré,Alexander Fedotov Pdf

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.

Author : R. N. Sen
Publisher : Cambridge University Press
Page : 413 pages
File Size : 43,9 Mb
Release : 2010-02-11
Category : Science
ISBN : 9781139485371

Get Book

Causality, Measurement Theory and the Differentiable Structure of Space-Time by R. N. Sen Pdf

Introducing graduate students and researchers to mathematical physics, this book discusses two recent developments: the demonstration that causality can be defined on discrete space-times; and Sewell's measurement theory, in which the wave packet is reduced without recourse to the observer's conscious ego, nonlinearities or interaction with the rest of the universe. The definition of causality on a discrete space-time assumes that space-time is made up of geometrical points. Using Sewell's measurement theory, the author concludes that the notion of geometrical points is as meaningful in quantum mechanics as it is in classical mechanics, and that it is impossible to tell whether the differential calculus is a discovery or an invention. Providing a mathematical discourse on the relation between theoretical and experimental physics, the book gives detailed accounts of the mathematically difficult measurement theories of von Neumann and Sewell.

Author : Gregory L. Naber
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 53,5 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475768503

Get Book

Topology, Geometry, and Gauge Fields by Gregory L. Naber Pdf

A study of topology and geometry, beginning with a comprehensible account of the extraordinary and rather mysterious impact of mathematical physics, and especially gauge theory, on the study of the geometry and topology of manifolds. The focus of the book is the Yang-Mills-Higgs field and some considerable effort is expended to make clear its origin and significance in physics. Much of the mathematics developed here to study these fields is standard, but the treatment always keeps one eye on the physics and sacrifices generality in favor of clarity. The author brings readers up the level of physics and mathematics needed to conclude with a brief discussion of the Seiberg-Witten invariants. A large number of exercises are included to encourage active participation on the part of the reader.

Author : D. Martin
Publisher : Elsevier
Page : 424 pages
File Size : 54,7 Mb
Release : 2002-03-01
Category : Mathematics
ISBN : 9780857099631

Get Book

Manifold Theory by D. Martin Pdf

This account of basic manifold theory and global analysis, based on senior undergraduate and post-graduate courses at Glasgow University for students and researchers in theoretical physics, has been proven over many years. The treatment is rigorous yet less condensed than in books written primarily for pure mathematicians. Prerequisites include knowledge of basic linear algebra and topology. Topology is included in two appendices because many courses on mathematics for physics students do not include this subject. Provides a comprehensive account of basic manifold theory for post-graduate students Introduces the basic theory of differential geometry to students in theoretical physics and mathematics Contains more than 130 exercises, with helpful hints and solutions

Author : Chris J Isham
Publisher : World Scientific Publishing Company
Page : 304 pages
File Size : 49,6 Mb
Release : 1999-03-19
Category : Science
ISBN : 9789813102965

Get Book

Modern Differential Geometry for Physicists by Chris J Isham Pdf

This edition of the invaluable text Modern Differential Geometry for Physicists contains an additional chapter that introduces some of the basic ideas of general topology needed in differential geometry. A number of small corrections and additions have also been made. These lecture notes are the content of an introductory course on modern, coordinate-free differential geometry which is taken by first-year theoretical physics PhD students, or by students attending the one-year MSc course “Quantum Fields and Fundamental Forces” at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen bearing in mind the way in which differential geometry is applied these days to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of Yang-Mills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field theory. The volume is divided into four parts: (i) introduction to general topology; (ii) introductory coordinate-free differential geometry; (iii) geometrical aspects of the theory of Lie groups and Lie group actions on manifolds; (iv) introduction to the theory of fibre bundles. In the introduction to differential geometry the author lays considerable stress on the basic ideas of “tangent space structure”, which he develops from several different points of view — some geometrical, others more algebraic. This is done with awareness of the difficulty which physics graduate students often experience when being exposed for the first time to the rather abstract ideas of differential geometry.

Author : Josi A. de Azcárraga,Josi M. Izquierdo
Publisher : Cambridge University Press
Page : 480 pages
File Size : 41,9 Mb
Release : 1998-08-06
Category : Mathematics
ISBN : 0521597005

Get Book

Lie Groups, Lie Algebras, Cohomology and Some Applications in Physics by Josi A. de Azcárraga,Josi M. Izquierdo Pdf

A self-contained introduction to the cohomology theory of Lie groups and some of its applications in physics.