The mathematical structure of classical and relativistic physics. A general classification diagram
The author studies the mathematical structure of classical and relativistic physics with a non-standard approach. He concentrates on the concepts such as global variables, field variables, oriented space elements, cell complexes, chains, cochains and coboundary operators for the description of classical and relativistic physics. Particle dynamics, electromagnetism, mechanics of deformable solids and mechanics of fluids are covered. Equilibrium thermodynamics, non-equilibrium thermodynamics, thermal conduction, gravitational fields and quantum mechanics are also touched. A detailed discussion of global variables versus field variables is provided. Inner and outer orientations of lines, surfaces and volumes are worked out in detail. The book also provides an enjoyable introduction to algebraic topology with applications to cell complexes and chains. Then, a number of applications to electrostatics are given. Furthermore, the logic of time reversal is also covered. The calculations are worked out in detail and often summarized in numerous diagrams, tables and figures. Reviewer's remark: Although differential forms and bivectors are mentioned in the book the reader would have like to seen a more deeper discussion about it, for example, why is it more beneficial to describe the electromagnetic field as differential two form \[ \beta = E_1dx_1 \wedge dt + E_2dx_2 \wedge dt + E_3dx_3 \wedge dt + B_1dx_2 \wedge dx_3 + B_2dx_3 \wedge dx_1 + B_3dx_1 \wedge dx_2 \] instead of the ``vectors'' \(\mathbf E\) and \(\mathbf B\). Nevertheless, the books can be highly recommended for readers from mathematics, physics and engineering, in particular for readers looking for an alternative approach to classical and relativistic physics.
scientific article; zbMATH DE number 6162131