Lectures On Elementary Particles And Quantum Field Theory 2 Lectures By Rudolph Haag

Lectures on elementary particles and quantum field theory. 2. Lectures by Rudolph Haag ...

Diffusion, Quantum Theory, and Radically Elementary Mathematics

Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion. It is also relevant to understanding various aspects of quantum theory. This book explains diffusive motion and its relation to both nonrelativistic quantum theory and quantum field theory. It shows how diffusive motion concepts lead to a radical reexamination of the structure of mathematical analysis. The book's inspiration is Princeton University mathematics professor Edward Nelson's influential work in probability, functional analysis, nonstandard analysis, stochastic mechanics, and logic. The book can be used as a tutorial or reference, or read for pleasure by anyone interested in the role of mathematics in science. Because of the application of diffusive motion to quantum theory, it will interest physicists as well as mathematicians. The introductory chapter describes the interrelationships between the various themes, many of which were first brought to light by Edward Nelson. In his writing and conversation, Nelson has always emphasized and relished the human aspect of mathematical endeavor. In his intellectual world, there is no sharp boundary between the mathematical, the cultural, and the spiritual. It is fitting that the final chapter provides a mathematical perspective on musical theory, one that reveals an unexpected connection with some of the book's main themes.

Quantum Particle Illusion, The - Conceptual Quantum Mechanics

Problems with the conceptual foundations of quantum mechanics date back to attempts by Max Born, Niels Bohr, Werner Heisenberg, as well as many others in the 1920s to continue to employ the classical concept of a particle in the context of the quantum world. The experimental observations at the time and the assumption that the classical concept of a particle was to be preserved have led to an enormous literature on the foundations of quantum mechanics and a great deal of confusion then and now among non-physicists and students in any field that involves quantum theory. It is the historical approach to the teaching of quantum mechanics that is at the root of the problem.Spacetime is the arena within which quantum mechanical phenomena take place. For this reason, several Appendices are devoted to the nature of spacetime as well as to topics that can help us understand it such as vacuum fluctuations, the Unruh effect and Hawking radiation.Because of the success of quantum mechanical calculations, those who wish to understand the foundations of the theory are often given the apocryphal advice, 'just ignore the issue and calculate'. It is hoped that this book will help dispel some of the dismay, frustration, and confusion among those who refuse to take to heart this admonition.