The Mathematical Structure of Classical and Relativistic Physics: A General Classification Diagram

ISBN-13: 9781461474210 / Angielski / Twarda / 2013 / 514 str.

Enzo Tonti

Opis

The theoriesdescribing seemingly unrelated areas of physics have surprising analogies that have arousedthe curiosity of scientists and motivatedefforts toidentify reasons for their existence.Comparative study of physical theories has revealed the presence of a common topological and geometric structure. "The Mathematical Structure of Classical and Relativistic Physics"is the first book to analyzethis structure in depth, thereby exposing the relationship between (a) global physical variables and (b) space and time elements such as points, lines, surfaces, instants, and intervals. Combining this relationship with the inner and outer orientation of space and time allows one to construct a classification diagram for variables, equations, and other theoretical characteristics.

The bookis divided into three parts. The first introduces the framework for the above-mentioned classification, methodically developingageometric and topologicalformulationapplicable to allphysical laws and properties; the second applies this formulation to a detailed study of particle dynamics, electromagnetism, deformable solids, fluid dynamics, heat conduction, and gravitation. The third part further analyses the general structure of the classification diagram for variables and equations of physical theories.

Suitable for a diverse audience of physicists, engineers, and mathematicians, "The Mathematical Structure of Classical and Relativistic Physics" offers a valuable resource for studying the physical world. Written at alevel accessible to graduate and advanced undergraduatestudents in mathematical physics, the book can be used as a research monograph across various areas of physics, engineering and mathematics, and as a supplemental text for a broad range of upper-level scientific coursework.

Recenzje

From the book reviews:

"The author studies the mathematical structure of classical and relativistic physics with a non-standard approach. ... 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." (Willi-Hans Steeb, zbMATH, Vol. 1298, 2014)

Spis treści

1 Introduction.- Part I Analysis of variables and equations.- 2 Terminology revisited.- 3 Space and time elements and their orientation.- 4 Cell complexes.- 5 Analysis of physical variables.- 6 Analysis of physical equations.- 7 Algebraic topology.- 8 The birth of the classification diagrams.- Part II Analysis of physical theories.- 9 Particle dynamics.- 10 Electromagnetism.- 11 Mechanics of deformable solids.- 12 Mechanics of fluids.- 13 Other physical theories.- Part III Advanced analysis.- 14 General structure of the diagrams.- 15 The mathematical structure.- Part IV Appendices.- A Affine vector fields.- B Tensorial notation.- C On observable quantities.- D History of the diagram.- D.1 Historical remarks.- E List of physical variables.- F List of symbols used in this book.- G List of diagrams.- References.