Tensors for Physics

- Introduction

- Basics

- Symmetry of Second Rank Tensors, Cross Product

- Epsilon-Tensor

- Symmetric Second Rank Tensors

- Summary: Decomposition of Second Rank Tensors

- Fields, Spatial Differential Operators

- Integration of Fields

- Irreducible Tensors

- Multiple Potentials

- Isotropic Tensors

- Integral Formulae

- Spin Operators

- Rotation of Tensors

- Liquid Crystals

- Constitutive Relations

- Tensor Dynamics

- Maxwell Equations, from 3D to 4D

- Exercises: Answers and Solutions

Siegfried Hess, was born in Hof, Germany, on March 20, 1940. He studied mathematics and physics at the University Erlangen-Nürnberg, where he also attended lectures in Astronomy and Chemistry. He received his PhD grade in 1967 and habilitated in 1970. From 1978 to 1984, he was a professor of theoretical physics at the University Erlangen-Nürnberg. In 1984 he became a professor at the Institute for Theoretical Physics of the Technical University Berlin (TUB). Since many years, he is a member of the German Physical Society (DFG), of the European Physical Society (EPS), of the Rheological Society (USA) and of the German Rheological Society. I was appointed as member of the Accademia Peloritana dei Pericolanti Messina, one of the oldest academic societies. He authored over 250 scientific publications, books, contributions to books and mostly articles in referred scientific journals, many written with about 100 coauthors, i.e. with students, postdocs and colleagues, from about 20 countries. His topics are the foundations of statistical physics and Non-Equilibrium Molecular Dynamics (NEMD) computer simulations, applications to the material properties of molecular gases, plasmas, simple and complex fluids, liquid crystals, polymeric liquids, magneto- and electro-rheological fluids, as well as to solid friction and plastic flow of metals.

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

"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 Radulescu, zbMATH 1320.00002, 2015)