Last edited by Yoran
Tuesday, May 5, 2020 | History

6 edition of Vector bundles in mathematical physics. found in the catalog.

Vector bundles in mathematical physics.

by Hermann, Robert

  • 169 Want to read
  • 6 Currently reading

Published by W. A. Benjamin in New York .
Written in English

    Subjects:
  • Vector bundles.,
  • Mathematical physics.

  • Edition Notes

    Bibliography: v. 1, p. 437-441; v. 2, p. 395-400.

    SeriesMathematics lecture note series, Mathematical physics monograph series.
    Classifications
    LC ClassificationsQA612.63 .H47
    The Physical Object
    Pagination2 v.
    ID Numbers
    Open LibraryOL5316179M
    ISBN 100805339450, 0805339493
    LC Control Number72135363

    This book intends to give the main definitions and theorems in mathematics which could be useful for workers in theoretical physics. It gives an extensive and precise coverage of the subjects which are addressed, in a consistent and intelligible first part addresses the Foundations (mathematical logic, set theory, categories), the second Algebra (algebraic strucutes, groups, vector Author: Jean Claude Dutailly. The plan is for this to be a fairly short book focusing on topological K-theory and containing also the necessary background material on vector bundles and characteristic classes. Here is a provisional Table of Contents. At present only about half of the book is in good enough shape to be posted online, approximately pages.

      In physics we have the concept of a vector field. Intuitively, a vector field is given by specifying a vector (in the sense of a quantity with magnitude and direction) at every point in a certain "space". For instance, the wind velocity on the surface of our planet is a vector field. If we neglect the. Author: P. K. Chattopadhyay; Publisher: New Age International ISBN: Category: Mathematical physics Page: View: DOWNLOAD NOW» The Book Is Intended As A Text For Students Of Physics At The Master S Level. It Is Assumed That The Students Pursuing The Course Have Some Knowledge Of Differential Equations And Complex Variables.

    A basic and extremely important structure in mathematical physics and in the results mentioned above is that of a vector bundle. Several physical theories such as Yang-Mills theory and Chern-Simons theory can be cast in terms of vector bundles. Moreover, natural bundles on manifolds such as the tangent and cotangent bundles are useful in. Introduction to Mathematical Physics The first few chapters of the book cover basic differential geometry, including the theory of manifolds, vector fields, and differential forms. These concepts are used to formulate Maxwell’s equations on arbitrary spacetime manifolds.


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Vector bundles in mathematical physics by Hermann, Robert Download PDF EPUB FB2

Additional Physical Format: Online version: Hermann, Robert, Vector bundles in mathematical physics. New York, W.A. Benjamin, (OCoLC) If the structure group of a vector bundle is reducible to \({GL(n,\mathbb{K})^{e}}\), then it is called an orientable bundle; all complex vector bundles are orientable, so orientability usually refers to real vector tangent bundle of \({M}\) (formally defined in an upcoming section) is then orientable iff \({M}\) is a pseudo-Riemannian manifold \({M}\), the structure.

Vector Bundles in Mathematical Physics. 2 Vols. Hardcover – January 1, by Robert Hermann (Author)Author: Robert Hermann. Vector bundles in mathematical physics, Volume 1 Mathematical physics monograph series Mathematics lecture note series: Author: Robert Hermann: Publisher: W.

Benjamin, Length: pages: Export Citation: BiBTeX EndNote RefMan. Vector bundles in mathematical physics/1. Hardcover – January 1, byAuthor: Robert Hermann. I'm personally a fan of Frankel's Geometry of Physics.

It's pretty fun speaking from both the perspective of a mathematician and a physicist. From a physics/engineering side, it covers all sorts of applications of differential geometry Vector bundles in mathematical physics. book all sort.

Vector bundles in mathematical physics, Volume 1 Issue 14 of Mathematical physics monograph series Mathematics lecture note series Vector Bundles in Mathematical Physics, Róbert Hermann: Author: Róbert Hermann: Publisher: W.

Benjamin, Original from: University of Minnesota: Digitized: Length: pages: Subjects. Get this from a library. Vector bundles in mathematical physics / [Robert Hermann]. C1 vector bundles arise naturally in modern physics, especially when the manifold M is spacetime or some extension of it.

When M is spacetime, its points may be thought of as representing the locations of particles. These particles obey the laws of quantum physics and therefore have a much richer internal structure than their classical.

Other articles where Vector bundle is discussed: mathematics: Mathematical physics and the theory of groups: is called the theory of vector bundles. Other kinds of space may be attached, thus entering the more general theory of fibre bundles.

The subtle and vital point is that it is possible to create quite different bundles which nonetheless look similar in small patches. Summary; Fiber bundles. Gauge theory.

Matter fields and gauges; The gauge potential and field strength; Spinor fields; Defining bundles. Fiber bundles; G-bundles; Principal bundles; Generalizing tangent spaces. Associated bundles; Vector bundles; Frame bundles; Gauge transformations on frame bundles; Smooth bundles and jets; Vertical tangents.

Abstract. Vector bundles constitute a special class of manifolds, which is of great importance in physics. In particular, all sorts of tensor fields occurring in physical models may be viewed in a coordinate-free manner as sections of certain vector bundles.

In mathematics and physics, a vector is an element of a vector space. For many specific vector spaces, the vectors have received specific names, which are listed below. Historically, vectors were introduced in geometry and physics (typically in mechanics) before the formalization of the concept of vector ore, one talks often of vectors without specifying the vector space to which.

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory.

e-books in Mathematical Physics category Lectures on Nonlinear Integrable Equations and their Solutions by A. Zabrodin -This is an introductory course on nonlinear integrable partial differential and differential-difference equations based on lectures given for students of Moscow Institute of Physics and Technology and Higher School of Economics.

This book is based on a two-semester sequence of courses taught to incoming graduate students at the University of Illinois at Urbana-Champaign, pri-marily physics students but also some from other branches of the physical sciences. The courses aim to introduce students to some of the mathematical.

The theory of partial differential equations (and the related areas of variational calculus, Fourier analysis, potential theory, and vector analysis) are perhaps most closely associated with mathematical were developed intensively from the second half of the 18th century (by, for example, D'Alembert, Euler, and Lagrange) until the s.

Classical mechanics without coordinates book. Ask Question Asked 9 years, 5 months ago. I can't help but think of the fields that arise in physics as sections of vector bundles (or maybe principal bundles) and would love an approach to classical mechanics or what have you that took advantage of this.

classical-mechanics mathematical. From the book reviews: “Mathematical Physics: A Modern Introduction to Its Foundations is intended for adoption in a course or a sequence of ‘methods of mathematical physics’ at the advanced undergraduate or beginning graduate level.

this is a textbook that every library must have (with a large number of copies in reserve), and it will be a valuable aid for committed students.

Fibre bundles play an important role in just about every aspect of modern geometry and topology. Basic properties, homotopy classification, and characteristic classes of fibre bundles have become an essential part of graduate mathematical education for students in geometry and mathematical : Springer-Verlag New York.

Vector bundles are locally free sheaves so I am trying to understand, in other words, the moduli space of locally free sheaves.

Now, if we include more general sheaves, not necessarily locally free, we get the moduli space of coherent (torsion free) sheaves.Vector Bundles in Algebraic Geometry | Successive waves of migrant concepts, largely from mathematical physics, have stimulated the study of vector bundles over algebraic varieties in the past few years.

But the subject has retained its roots in old questions concerning subvarieties of projective space.This book provides a working knowledge of those parts of exterior differential forms, differential geometry, algebraic and differential topology, Lie groups, vector bundles and Chern forms that are essential for a deeper understanding of both classical and modern physics and by: