Related papers: Fundamental Topics in Continuum Mechanics: Grand I…
In 1946, Garrett Birkhoff proved that the $n\times n$ doubly stochastic matrices comprise the convex hull of the $n\times n$ permutation matrices, which in turn make up the extreme points of this polytope. He proposed his problem 111, which…
The textbook contains the problems in mechanics and special relativity for physics departments of universities. Many original problems were proposed by active scientists from the institutes of the Siberian Branch of Russian Academy of…
This is the translation to appear in the "SUPERSYMMETRY 2000 - Encyclopaedic Dictionary" of the original paper, published in March 1980, (C.R. Acad. Sci. Paris, Ser. A-B, 290, 1980) in which basic notions of noncommutative geometry were…
The concept of frames, initially introduced by Duffin and Schaeffer, gained substantial recognition decades later when Daubechies, Grossman, and Meyer highlighted its significance. Since then, frame theory has become a fundamental and…
If the statement by Einstein, Podolsky and Rosen on incompleteness of Quantum-Mechanical description of nature is correct, then we can regard Quantum Mechanics as a Method of Indirect Computation. The problem is, whether the theory is…
The major advances in physics have been through counterintuitive breakthroughs-- ideas that seemed to go against prevailing convictions. In the twentieth century the Special and General Theory of Relativity and Quantum Mechanics have…
This is an English translation of the Italian version of an encyclopedia chapter that appeared in the Italian Encyclopedia of the Physical Sciences, edited by Bruno Bertotti (1994). Following requests from colleagues we have decided to make…
An informal guide to the history of Heisenberg's matrix mechanics. It is designed for mathematicians with only a minimal background in either physics or geometry, and it is based upon Heisenberg's original arguments.
We give, for the first time, the English translation of a manuscript by Ettore Majorana, which probably corresponds to the text for a seminar delivered at the University of Naples in 1938, where he lectured on Theoretical Physics. Some…
This is the first chapter of a new and unconventional textbook on quantum mechanics and quantum field theory. The chapter introduces standard quantum mechanics by means of a symmetry principle, without reference to classical mechanics. The…
Bogoliubov's 1947 approximation, originally developed in the microscopic theory of superfluidity, laid the foundation for solving previously intractable quantum models and later became part of "quantum mathematics". Regarding mathematically…
Despite being known for his pioneering work on chaotic unpredictability, the key discovery at the core of meteorologist Ed Lorenz's work is the link between space-time calculus and state-space fractal geometry. Indeed, properties of…
Invariant integration of vectors and tensors over manifolds was introduced around fifty years ago by V.N. Folomeshkin, though the concept has not attracted much attention among researchers. Although it is a sophisticated concept, the…
These notes grew out of a lecture course on mathematical methods of classical physics for students of mathematics and mathematical physics at the master's level. Also, physicists with a strong interest in mathematics may find this text…
This paper is a commentary on Rudolph Peierls's "In defence of measurement" Physics World 19-20, January 1991 to accompany the reprint of this paper for the special volume dedicated to the celebration of the centenary of the discovery of…
The aim of this set of lectures is a systematic presentation of a 1+3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic 1+3 covariant relations…
English translation of John von Neumann's 1927 trilogy on the foundations of quantum mechanics with an introduction and detailed commentary.
Maxwell's mature presentation of his equations emphasized the unity of electromagnetism and mechanics, subsuming both as "dynamical systems". That intuition of unity has proved both fruitful, as a source of pregnant concepts, and broadly…
This chapter is dedicated to the so-called cuspidal robots, i.e. those robots that can move from one inverse geometric solution to another without meeting a singular confuguration. This feature was discovered quite recently and has then…
This book includes my lectures, together with their problem sets and solutions, on 1) classical mechanics (one semester), 2) thermodynamics and statistical mechanics (one semester), and 3) quantum mechanics (one semester), which I have been…