Lie Pseudogroups and Mechanics (Hardcover)

This book outlines the fact that effective progress in mathematical physics is always produced by new mathematical concepts replacing old physical intuitions.;It begins with a history of the relations that have existed between geometry and physics through the respective developments of group theory and field theory, and goes on to demonstrate that the Cartan approach to group theory is based on a confusion between two differential sequences in the formal theory of systems of partial differential equations and lie pseudogroups. Pommaret proves that this confusion stems from Cartan's deliberate omission of Vessiot's and Janet's work. He also shows that correcting this mathematical confusion leads to a re-examination of the foundations of many physical theories, including continuum, mechanics, thermodynamics, gauge theory and general relativity. In particular, he gives for the first time a modern exposition of E.Cosserat and F.Cosserat's elasticity theory in relation to the work of D.C.Spencer on lie pseudogroups.