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  • Textbook
  • © 2015

Tensors for Physics

Authors:

  • Supports learning and teaching with extended exercises at the end of every chapter including solutions
  • Contains numerous examples for efficient description of anisotropies in physical phenomena
  • Describes how to use tensors to calculate anisotropical properties of orientational phenomena in the theoretical description, in addition to vector analysis
  • Presents vector analysis using Cartesian components
  • Contains a chapter on the physics of liquid crystals, the best model application of the tensor algebra
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (18 chapters)

  1. Front Matter

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

    1. Front Matter

      Pages 1-1
    2. Introduction

      • Siegfried Hess
      Pages 3-9
    3. Basics

      • Siegfried Hess
      Pages 11-32
    4. Epsilon-Tensor

      • Siegfried Hess
      Pages 47-54
    5. Symmetric Second Rank Tensors

      • Siegfried Hess
      Pages 55-74
    6. Fields, Spatial Differential Operators

      • Siegfried Hess
      Pages 77-109
    7. Integration of Fields

      • Siegfried Hess
      Pages 111-152
  3. Advanced Topics

    1. Front Matter

      Pages 153-153
    2. Irreducible Tensors

      • Siegfried Hess
      Pages 155-162
    3. Multipole Potentials

      • Siegfried Hess
      Pages 163-181
    4. Isotropic Tensors

      • Siegfried Hess
      Pages 183-197
    5. Integral Formulae and Distribution Functions

      • Siegfried Hess
      Pages 199-238
    6. Spin Operators

      • Siegfried Hess
      Pages 239-257
    7. Rotation of Tensors

      • Siegfried Hess
      Pages 259-271
    8. Liquid Crystals and Other Anisotropic Fluids

      • Siegfried Hess
      Pages 273-298
    9. Constitutive Relations

      • Siegfried Hess
      Pages 299-350
    10. Tensor Dynamics

      • Siegfried Hess
      Pages 351-368

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.

Reviews

“This book is devoted to a thorough didactic presentation of tensors, which play an important role in Physics in order to describe anisotropic phenomena and their orientational behavior. … This volume is very well written and it can be a valuable support to researchers and graduate students in mathematical physics, applied nonlinear analysis and other applied sciences.” (Teodora-Liliana Rădulescu, zbMATH 1320.00002, 2015)

Authors and Affiliations

  • Institute for Theoretical Physics, Technical University Berlin, Berlin, Germany

    Siegfried Hess

About the author

Siegfried Hess studied Mathematics and Physics at the University Erlangen-Nürnberg, was a graduate student in Chemical Engineering at the University of  Minnesota in Minneapolis, USA and  got his PhD in Physics in Erlangen in 1967. He was postdoc at the Kamerlingh Onnes Laboratory of the University Leiden, Holland and made his habilitation in Physics in Erlangen, 1970. Later, he became professor for Theoretical Physics in Erlangen and from 1984 till 2007 he held the chair for Transport Theory and Statistical Physics at the Institute for Theoretical Physics of the Technical University Berlin. As guest scientist and visiting professor he worked at the Department of Physics of the University of Toronto, Canada,  at the Huygens Laboratory of the University Leiden, at the National Bureau of Standards (NBS, now NIST) in Boulder, Colorado, USA, at the Institute Laue-Langevin in Grenoble, France, at the department of Chemistry of the National Australian University in Canberra and at the Institute for Theoretical Physics (ITP, now KITP) of the University of California in Santa Barbara.
Siegfried Hess was involved in numerous national and international research projects, both as project leader and as reviewer and adviser. His scientific work is documented in over 250 publications. The list of publications features the names of over 100 co-authors, viz. of students,  postdocs and colleagues, from about 20 countries and of all 5 continents.   He was fond of demonstrating the advantages of the use of Cartesian Tensors in teaching the courses of Theoretical Physics and in his research dealing with equilibrium and non-equilibrium properties of anisotropic fluids and other topics of condensed matter physics.

Bibliographic Information

Buy it now

Buying options

eBook USD 59.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 79.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access