Tensors for Physics

  • Siegfried Hess

Part of the Undergraduate Lecture Notes in Physics book series (ULNP)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. A Primer on Vectors and Tensors

    1. Front Matter
      Pages 1-1
    2. Siegfried Hess
      Pages 3-9
    3. Siegfried Hess
      Pages 11-32
    4. Siegfried Hess
      Pages 47-54
    5. Siegfried Hess
      Pages 55-74
    6. Siegfried Hess
      Pages 77-109
    7. Siegfried Hess
      Pages 111-152
  3. Advanced Topics

    1. Front Matter
      Pages 153-153
    2. Siegfried Hess
      Pages 155-162
    3. Siegfried Hess
      Pages 163-181
    4. Siegfried Hess
      Pages 183-197
    5. Siegfried Hess
      Pages 199-238
    6. Siegfried Hess
      Pages 239-257
    7. Siegfried Hess
      Pages 259-271
    8. Siegfried Hess
      Pages 273-298
    9. Siegfried Hess
      Pages 299-350
    10. Siegfried Hess
      Pages 351-368
  4. Back Matter
    Pages 389-440

About this book


This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics,  at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to  tensors of any rank, at graduate level.  Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-trace formulas, coupling of irreducible tensors, rotation of tensors. Constitutive laws for optical, elastic and viscous properties of anisotropic media are dealt with.  The anisotropic media include crystals, liquid crystals and isotropic fluids, rendered anisotropic  by external orienting fields. The dynamics of tensors deals with phenomena of current research.  In the last section,  the 3D Maxwell equations are reformulated in their 4D version,  in accord with special relativity.


Anistropic Physical Properties Cartesian Tensors Irreducible Tensors Isotropic Tensors Rotation of Tensors Second Rank Tensors Spin Tensors Tensor Algebra and Analysis Tensor Dynamics Tensors in Electrodynamics

Authors and affiliations

  • Siegfried Hess
    • 1
  1. 1.Institute for Theoretical PhysicsTechnical University BerlinBerlinGermany

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-12786-6
  • Online ISBN 978-3-319-12787-3
  • Series Print ISSN 2192-4791
  • Series Online ISSN 2192-4805
  • Buy this book on publisher's site
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