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Quantum Mathematical Physics
Quantum physics has been highly successful for more than 90 years. Nevertheless, a rigorous construction of interacting quantum field theory is still missing. Moreover, it is still unclear how to combine quantum physics and general relativity in a unified physical theory. Attacking these challenging problems of contemporary physics requires highly advanced mathematical methods as well as radically new physical concepts. This book presents different physical ideas and mathematical approaches in this direction. It contains a carefully selected cross-section of lectures which took place in autumn 2014 at the sixth conference ``Quantum Mathematical Physics - A Bridge between Mathematics and Physics'' in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.
Quantum Physics Without Quantum Philosophy
It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrödinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Physics Meets Philosophy at the Planck Scale
Was the first book to examine the exciting area of overlap between philosophy and quantum mechanics with chapters by leading experts from around the world.
Mathematical Physics: Classical Mechanics
As a limit theory of quantum mechanics, classical dynamics comprises a large variety of phenomena, from computable (integrable) to chaotic (mixing) behavior. This book presents the KAM (Kolmogorov-Arnold-Moser) theory and asymptotic completeness in classical scattering. Including a wealth of fascinating examples in physics, it offers not only an excellent selection of basic topics, but also an introduction to a number of current areas of research in the field of classical mechanics. Thanks to the didactic structure and concise appendices, the presentation is self-contained and requires only knowledge of the basic courses in mathematics. The book addresses the needs of graduate and senior undergraduate students in mathematics and physics, and of researchers interested in approaching classical mechanics from a modern point of view.
Mathematical Results in Quantum Physics
The volume collects papers from talks given at QMath11 - Mathematical Results in Quantum Physics, which was held in Hradec Kralove, September 2010. These papers bring new and interesting results in quantum mechanics and information, quantum field theory, random systems, quantum chaos, as well as in the physics of social systems. Part of the contribution is dedicated to Ari Laptev on the occasion of his 60th birthday, in recognition of his mathematical results and his service to the community. The QMath conference series has played an important role in mathematical physics for more than two decades, typically attracting many of the best results achieved in the last three-year period, and the meeting in Hradec Kralove was no exception.
Geometric and Computational Spectral Theory
A co-publication of the AMS and Centre de Recherches Mathématiques The book is a collection of lecture notes and survey papers based on the mini-courses given by leading experts at the 2015 Séminaire de Mathématiques Supérieures on Geometric and Computational Spectral Theory, held from June 15–26, 2015, at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. The volume covers a broad variety of topics in spectral theory, highlighting its connections to differential geometry, mathematical physics and numerical analysis, bringing together the theoretical and computational approaches to spectral theory, and emphasizing the interplay between the two.
David Bohm
This authoritative biography addresses the life and work of the quantum physicist David Bohm. Although quantum physics is considered the soundest physical theory, its strange and paradoxical features have challenged - and continue to challenge - even the brightest thinkers. David Bohm dedicated his entire life to enhancing our understanding of quantum mysteries, in particular quantum nonlocality. His work took place at the height of the cultural/political upheaval in the 1950's, which led him to become the most notable American scientist to seek exile in the last century. The story of his life is as fascinating as his ideas on the quantum world are appealing.
Foundations of Quantum Mechanics
This book introduces and critically appraises the main proposals for how to understand quantum mechanics, namely the Copenhagen interpretation, spontaneous collapse, Bohmian mechanics, many-worlds, and others. The author makes clear what are the crucial problems, such as the measurement problem, related to the foundations of quantum mechanics and explains the key arguments like the Einstein-Podolsky-Rosen argument and Bell’s proof of nonlocality. He discusses and clarifies numerous topics that have puzzled the founding fathers of quantum mechanics and present-day students alike, such as the possibility of hidden variables, the collapse of the wave function, time-of-arrival measurements, explanations of the symmetrization postulate for identical particles, or the nature of spin. Several chapters are devoted to extending the different approaches to relativistic space-time and quantum field theory. The book is self-contained and is intended for graduate students and researchers who want to step into the fundamental aspects of quantum physics. Given its clarity, it is accessible also to advanced undergraduates and contains many exercises and examples to master the subject.
Spectral Analysis on Graph-like Spaces
Small-radius tubular structures have attracted considerable attention in the last few years, and are frequently used in different areas such as Mathematical Physics, Spectral Geometry and Global Analysis. In this monograph, we analyse Laplace-like operators on thin tubular structures ("graph-like spaces''), and their natural limits on metric graphs. In particular, we explore norm resolvent convergence, convergence of the spectra and resonances. Since the underlying spaces in the thin radius limit change, and become singular in the limit, we develop new tools such as norm convergence of operators acting in different Hilbert spaces, an extension of the concept of boundary triples to partial differential operators, and an abstract definition of resonances via boundary triples. These tools are formulated in an abstract framework, independent of the original problem of graph-like spaces, so that they can be applied in many other situations where the spaces are perturbed.
Mathematical Results In Quantum Physics - Proceedings Of The Qmath11 (With Dvd-rom)
The volume collects papers from talks given at QMath11 — Mathematical Results in Quantum Physics, which was held in Hradec Králové, September 2010. These papers bring new and interesting results in quantum mechanics and information, quantum field theory, random systems, quantum chaos, as well as in the physics of social systems. Part of the contribution is dedicated to Ari Laptev on the occasion of his 60th birthday, in recognition of his mathematical results and his service to the community. The QMath conference series has played an important role in mathematical physics for more than two decades, typically attracting many of the best results achieved in the last three-year period, and the meeting in Hradec Králové was no exception.
