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Quantum Mechanics in Phase Space
Wigner's quasi-probability distribution function in phase space is a special (Weyl) representation of the density matrix. It has been useful in describing quantum transport in quantum optics; nuclear physics; decoherence, quantum computing, and quantum chaos. It is also important in signal processing and the mathematics of algebraic deformation. A remarkable aspect of its internal logic, pioneered by Groenewold and Moyal, has only emerged in the last quarter-century: it furnishes a third, alternative, formulation of quantum mechanics, independent of the conventional Hilbert space, or path integral formulations.In this logically complete and self-standing formulation, one need not choose side...
Quantum Theory and Symmetries with Lie Theory and Its Applications in Physics Volume 2
This book is the second volume of the proceedings of the joint conference X. International Symposium “Quantum Theory and Symmetries” (QTS-X) and XII. International Workshop “Lie Theory and Its Applications in Physics” (LT-XII), 19–25 June 2017, Varna, Bulgaria. The QTS series started around the core concept that symmetries underlie all descriptions of quantum systems. It has since evolved into a symposium on the frontiers of theoretical and mathematical physics. The LT series covers the whole field of Lie Theory in its widest sense together with its applications in many facets of physics. As an interface between mathematics and physics the workshop serves as a meeting place for mat...
Physics and Necessity
This book recounts a few ingenious attempts to derive physical theories by reason only, beginning with Descartes' geometric construction of the world, and finishing with recent derivations of quantum mechanics from natural axioms.
Argonne News
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Maverick Mathematician
"J.E. Moyal has been pronounced 'one of Australia's most remarkable thinkers'. Yet, he was, essentially, a scientific maverick. Educated in a modest high school in Tel Aviv, he took himself to France to train as an engineer, statistician and mathematician and escaped to England as France fell. It was from outside academia that he entered into communication with the 'high priest' of British theoretical physics, P.A.M. Dirac, challenging him with the idea of a statistical basis of quantum mechanics. Their correspondence forms the core of this book and opens up an important and hitherto unknown chapter for physicists, mathematicians and historians of science. Moyal's classic paper, 'A statistical basis for quantum mechanics', also reproduced here in full, has come to underlie an explosion of research and to underpin an array of major technological developments."--Publisher's description.
Symmetries in Science V
Proceedings of a symposium held in Landesbildungszentrum Schloss Hofen, Lochau, Vorarlberg, Austria, July 30-August 3, 1990
Real and Complex Singularities
This volume is a collection of papers presented at the XIII International Workshop on Real and Complex Singularities, held from July 27–August 8, 2014, in São Carlos, Brazil, in honor of María del Carmen Romero Fuster's 60th birthday. The volume contains the notes from two mini-courses taught during the workshop: on intersection homology by J.-P. Brasselet, and on non-isolated hypersurface singularities and Lê cycles by D. Massey. The remaining contributions are research articles which cover topics from the foundations of singularity theory (including classification theory and invariants) to topology of singular spaces (links of singularities and semi-algebraic sets), as well as applications to topology (cobordism and Lefschetz fibrations), dynamical systems (Morse-Bott functions) and differential geometry (affine geometry, Gauss-maps, caustics, frontals and non-Euclidean geometries). This book is published in cooperation with Real Sociedad Matemática Española (RSME)
The Oxford Handbook of the History of Quantum Interpretations
Crucial to most research in physics, as well as leading to the development of inventions such as the transistor and the laser, quantum mechanics approaches its centenary with an impressive record. However, the field has also long been the subject of ongoing debates about the foundations and interpretation of the theory, referred to as the quantum controversy. This Oxford Handbook offers a historical overview of the contrasts which have been at the heart of quantum physics for the last 100 years. Drawing on the wide-ranging expertise of several contributors working across physics, history, and philosophy, the handbook outlines the main theories and interpretations of quantum physics. It goes ...
Advances in Applied Analysis
This book contains survey papers based on the lectures presented at the 3rd International Winter School “Modern Problems of Mathematics and Mechanics” held in January 2010 at the Belarusian State University, Minsk. These lectures are devoted to different problems of modern analysis and its applications. An extended presentation of modern problems of applied analysis will enable the reader to get familiar with new approaches of mostly interdisciplinary character. The results discussed are application oriented and present new insight into applied problems of growing importance such as applications to composite materials, anomalous diffusion, and fluid dynamics.
