Advertisement

Vector and tensor fields

  • James Foster
  • J. David Nightingale

Abstract

In this first chapter we concentrate on the algebra of vector and tensor fields, while postponing ideas that are based on the calculus of fields to Chapter 2. Our starting point is a consideration of vector fields in the familiar setting of three-dimensional Euclidean space and how they can be handled using arbitrary curvilinear coordinate systems. We then go on to extend and generalize these ideas in two different ways, first by admitting tensor fields, and second by allowing the dimension of the space to be arbitrary and its geometry to be non-Euclidean.1 The eventual goal is to present a model for the spacetime of general relativity as a four-dimensional space that is curved, rather than fiat. While some aspects of this model emerge in this chapter, it is more fully developed in Chapters 2 and 3, where we introduce some more mathematical apparatus and relate it to the physics of gravitation.

Keywords

Euclidean Space Basis Vector Tangent Vector Tensor Field Natural Basis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • James Foster
    • 1
  • J. David Nightingale
    • 2
  1. 1.School of Mathematical SciencesUniversity of SussexFalmer, BrightonUK
  2. 2.Department of Physics, The College at New PaltzState University of New YorkNew PaltzUSA

Personalised recommendations