Last edited by Bahn
Saturday, May 9, 2020 | History

5 edition of Fibre bundle techniques in gauge theories found in the catalog.

Fibre bundle techniques in gauge theories

by Drechsler, Wolfgang

  • 136 Want to read
  • 38 Currently reading

Published by Springer-Verlag in Berlin, New York .
Written in English

    Subjects:
  • Gauge fields (Physics),
  • Fiber bundles (Mathematics)

  • Edition Notes

    Includes bibliographical references.

    StatementW. Drechsler, M. E. Mayer.
    SeriesLecture notes in physics ;, 67
    ContributionsMayer, Meinhard E. 1929- joint author.
    Classifications
    LC ClassificationsQC793.3.F5 D73
    The Physical Object
    Paginationix, 248 p. ;
    Number of Pages248
    ID Numbers
    Open LibraryOL4554258M
    ISBN 100387083502
    LC Control Number77023936

    geometry of principal bundles leads to a ber bundle interpretation of Yang-Mills theory. Doing so is the principal goal of the present paper.3 My basic strategy will be to exploit an analogy between Yang-Mills theory and general relativity, where I take it we are on rmer ground.4 The mathematical facts on which theFile Size: KB. Discover Book Depository's huge selection of Wolfgang Drechsler books online. Free delivery worldwide on over 20 million titles. Fiber Bundle Techniques in Gauge Theories. Wolfgang Drechsler. 01 Jul Porträts. Wolfgang Drechsler. Paperback. unavailable. Try AbeBooks. Fibre Bundle Techniques in Gauge Theories. Wolfgang Drechsler.

    Gauge theory usually investigates the space of principal connections on a principal fiber bundle (P,p,M,G) and its orbit space under the action of the gauge group (called the moduli space), which is the group of all principal bundle automorphisms of P which cover the identity on the base space M. It is the arena for the Yang-Mills-Higgs equa-File Size: KB. Fibre bundle is a very interesting manifold and is formed by combining a manifold M with all its tangent spaces. A fibre bundle is a manifold that looks locally like a product of two manifolds.

    Fiber Bundles, Gauge Theories and Gravity 6 Will-be-set-by-IN-TECH Obviously, the reconstruction of the whole class of connections along a fiber is obtained from. 5 Vector Potential as Connection on a Fiber. Bundle. Mathematicians have studied the abstract concept of connections on fiber bundles since the ’s. A number of scattered papers in the ’s and ’s have pointed out that gauge theories are related to this concept.


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Fibre bundle techniques in gauge theories by Drechsler, Wolfgang Download PDF EPUB FB2

Most historical accounts in the gauge theory literature about the early history of the link-up between gauge theory physics and fibre bundle mathematics refer to this as one of the earliest developments, but these lectures are still a valuable introduction.

They are referred to for their contents as much as for their historical value. Cited by: 1. Fiber bundle techniques in gauge theories (Lecture notes in physics) Paperback – January 1, Most historical accounts in the gauge theory literature about the early history of the link-up between gauge theory physics and fibre bundle mathematics refer to this as one of the earliest developments, but these lectures are still a valuable Cited by: Fiber Bundle Techniques in Gauge Theories Lectures in Mathematical Physics at the University of Texas at Austin.

Authors: Drechsler, W., Mayer, M.E. Editors: Böhm, A. The underlying mathematical structures of gauge theories are known to be geomet-rical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles.

It is now understood that the global properties of gauge theories can have a profound influence on physics. ForFile Size: KB. Fibre bundle techniques in gauge theories.

Berlin ; New York: Springer-Verlag, (DLC) (OCoLC) Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors: Wolfgang Drechsler; Meinhard E. the mathematics of fibre bundles in the understanding of some global aspects of gauge theories, such as monopoles and instantons.

They are primarily aimed at beginning PhD students. First, we will briefly review the concept of a fibre bundle and define the notion of a connection and its curvature on a principal by: 6.

In physics, a gauge theory is a type of field theory in which the Lagrangian does not change (is invariant) under local transformations from certain Lie groups. The term gauge refers to any specific mathematical formalism to regulate redundant degrees of freedom in the Lagrangian.

The transformations between possible gauges, called gauge transformations, form a Lie. Two aspects of bundles in physics come together in the theory of gauge fields and combine to produce higher fiber bundles: namely we saw above that a gauge field is itself already a bundle (with a connection), and hence the bundle of which a gauge field is a .Fibre bundle techniques in gauge theories / W.

Drechsler, M. Mayer Springer-Verlag Berlin ; New York Wikipedia Citation Please see Wikipedia's template documentation for further citation fields that may be required.

Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Good Books on Gauge Theory [duplicate] Ask Question Asked 7 years, Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource.

Instead of focusing on specifically fibre bundles, I want to talk to you about bundles in general. Fibre bundles become very easy and intuitive once one has a grasp on the general machinery of bundle theory. Let’s say you have some sort of space. In mathematics, and particularly topology, a fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological ically, the similarity between a space and a product space × is defined using a continuous surjective map: → that in small regions of E behaves just like a projection from.

The tangent bundle of Projective Space 24 K - theory 25 Differential Forms 30 Connections and Curvature 33 The Levi - Civita Connection 39 Chapter 2. Classification of Bundles 45 1. The homotopy invariance of fiber bundles 45 2. Universal bundles and classifying spaces 50 3.

Classifying Gauge Groups 60 Size: KB. Book: Fiber bundle techniques in gauge theories Springer, ISBN, My Amazon review. pages. Two sets of lecture notes in one book. Introduction to the fiber-bundle approach to gauge theories, Meinhard Edwin Mayer, pages 1– Given in Austin, TexasIrvine, California /76, Aspen Center for.

Bundles & Gauges, a Math-Physics Duality - the case of Gravity - David Mendes A modern and straight forward summary of the necessary tools and concepts needed to understand and work with gauge theory in a fibre bundle formalism.

Due to the aim of being a quick but thorough introduction full derivations are rarely included, but. Since the excellent and clear article by Prof. Edward Frenkel inspiring this question focuses on my joint work with the economist Pia Malaney, I would be happy to say a few words here.

This may be considered a brief sketch of our program through. To better understand papers like this for example, which makes heavy use of fibre bundles and gauge connections to represent gauge fields, I am looking for a nice introduction to this topic.

The only thing I have read so far is the corresponding chapter 15 of Roger Penrose's "Road to Reality". I do not want to read a whole book, I am rather thinking about an appropriate.

A bundle {E,π,B,F,G} is said to be reducible if one may restric the transition func-tions gij to lie in a subgroup H of the structural group G to obtain a new bundle {E′,π′,B,F′,H} with the same base B. Reduction of the frame bundle The frame bundle F(M) is a principal bundle with structural group GL(n,R becauseFile Size: KB.

A gauge field being a connection on a fibre bundle is only described locally as a Lie algebra valued one form. Although this representation is used in the formulation of the various action functionals in quantum field theory, one must always remember that this formulation is only local.

Fiber bundles are widely used in gauge theories. The fibers are various Lie groups. The simplest one is the [math]U(1)[/math] bundle describing the electromagnetic field. A charged particle is described as a complex field [math]\Phi(x)[/math].

tors on a Hilbert space, and in gauge theories such as electro­ magnetism and Yang-Mills particle fields, the connection ap­ pears as a continuous choice of gauge at each point in space.

time. Here, connections in general relativity and geometric quantization are dealt with briefly; for a discussion of gauge theories, see [: Barry Jessup.

Introduction to the fiber-bundle approach to gauge theories. Chapter. First Online: 05 August 3 Introduction to the fiber-bundle approach to gauge theories. In: Drechsler W., Mayer M.E., Böhm A., Dollard J.D. (eds) Fiber Bundle Techniques in Gauge Theories.

Lecture Notes in Physics, vol Springer, Berlin, Heidelberg. First Online.This chapter discusses the implications of gauge theories for our conception of properties, and for the reality of fibre-bundle spaces.

One way of understanding such theories is to claim that the only way in which properties at different locations can be compared is to ‘drag’ these properties to one and the same location, and then locally compare them.