Courant, Hilbert - Methods of Mathematical Physics Vol. II

2018

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Cover photo: Archives of the Mathematisches Forschungsinstitut Oberwolfach

Notices of the American Mathematical Society, 2019

The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.

Axioms

Mathematical physics has many facets, of which we shall briefly give a (very partial) description, centered around those of main interest for Elliott and us (Moshe Flato and I), and around the seminal scientific and personal interactions that developed between us since the sixties until Moshe’s untimely death in 1998. These aspects still influence my scientific activity and my life. They also had as a corollary a variety of “parascientific activities”, in particular, the foundation of IAMP (the International Association of Mathematical Physics) and of the journal LMP (Letters in Mathematical Physics), both of which were strongly impacted by Elliott, and Elliott’s long insistence that publishers do not demand “copyright transfer” as a precondition for publication but are satisfied with a “consent to publish”, which is increasingly becoming standard. This article being mainly a testimony to the huge scientific impacts of Elliott and also of Moshe, their intertwined aspects constitute ...

This e-book introduces a series of new theoretical mathematical frameworks designed for applications in physics and pure sciences. The primary objective is to provide robust support for, or investigate, various theories and experiments.

arXiv: Mathematical Physics, 2011

The present issue of the series > represents the Proceedings of the Students Training Contest Olympiad in Mathematical and Theoretical Physics and includes the statements and the solutions of the problems offered to the participants. The contest Olympiad was held on May 21st-24th, 2010 by Scientific Research Laboratory of Mathematical Physics of Samara State University, Steklov Mathematical Institute of Russia's Academy of Sciences, and Moscow Institute of Physics and Technology (State University) in cooperation. The present Proceedings is intended to be used by the students of physical and mechanical-mathematical departments of the universities, who are interested in acquiring a deeper knowledge of the methods of mathematical and theoretical physics, and could be also useful for the persons involved in teaching mathematical and theoretical physics.

Journal of Mathematical Physics, 2010

2013

Wigner's quasi-probability distribution function in phase-space is a special (Weyl-Wigner) representation of the density matrix. It has been useful in describing transport in quantum optics, nuclear physics, quantum computing, decoherence, and chaos. It is also of importance 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 sides between coordinate or momentum space. It works in full phase-space, accommodating the uncertainty principle; and it offers unique insights into the classical limit of quantum theory: The variables (observables) in this formulation are c-number functions in phase space instead of operators, with the same interpretation as their classical counterparts, but are composed together in novel algebraic ways. This treatise provides an introductory overview and includes an extensive bibliography. Still, the bibliography makes no pretense to exhaustiveness. The overview collects often-used practical formulas and simple illustrations, suitable for applications to a broad range of physics problems, as well as teaching. As a concise treatise, it provides supplementary material which may be used for an advanced undergraduate or a beginning graduate course in quantum mechanics. It represents an expansion of a previous overview with selected papers collected by the authors, and includes a historical narrative account due the subject. This Historical Survey is presented first, in Section 1, but it might be skipped by students more anxious to get to the mathematical details beginning with the Introduction in Section 2. Alternatively, Section 1 may be read alone by anyone interested only in the history of the subject. Peter Littlewood and Harry Weerts are thanked for allotting time to make the treatise better.

Lecture Notes in Physics, 1978