Groups Invariants Integrals And Mathematical Physics
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Groups, Invariants, Integrals, and Mathematical Physics
This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include: The multisymplectic and variational nature of Monge-Ampère equations in dimension four Integrability of fifth-order equations admitting a Lie symmetry algebra Applications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfaces A geometric framework to compare classical systems of PDEs in the category of smooth manifolds Groups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed.
Golden Age Of Theoretical Physics, The (Boxed Set Of 2 Vols)
The Golden Age of Theoretical Physics brings together 37 selected essays. Many of these essays were first presented as lectures at various universities in Europe and the USA, and then published as reports or articles. Their enlarged, final versions were published in the joint work of Jagdish Mehra and Helmut Rechenberg, The Historical Development of Quantum Theory, while the other essays were published as articles in scientific journals or in edited books. Here they are published together as a tribute to the Mehra-Rechenberg collaboration sustained for several decades, and cover various aspects of quantum theory, the special and general theories of relativity, the foundations of statistical mechanics, and some of their fundamental applications. Two essays, ‘Albert Einstein's “First” Paper’ (Essay 1) and ‘The Dream of Leonardo da Vinci’ (Essay 37), lie outside the major themes treated in this book, but are included here because of their historical interest. The origin of each essay is explained in a footnote.This book deals with the most important themes developed in the first 40 years of the twentieth century by some of the greatest pioneers and architects of modern physics. It is a vital source of information about what can veritably be described as ‘the golden age of theoretical physics’.
Group-Theoretic Methods in Mechanics and Applied Mathematics
Group analysis of differential equations has applications to various problems in nonlinear mechanics and physics. Group-Theoretic Methods in Mechanics and Applied Mathematics systematizes the group analysis of the main postulates of classical and relativistic mechanics. Exact solutions are given for the following equations: dynamics of rigid body, heat transfer, wave, hydrodynamics, Thomas-Fermi, and more. The author pays particular attention to the application of group analysis to developing asymptotic methods for problems with small parameters. This book is designed for a broad audience of scientists, engineers, and students in the fields of applied mathematics, mechanics and physics.