In recent years, there has been an increased interest in exploring the connections between various disciplines of mathematics and theoretical physics such as representation theory, algebraic geometry, quantum field theory, and string theory. One of the challenges of modern mathematical physics is to understand rigorously the idea of quantization. The program of quantization by branes, which com…
This biography explores the life and career of the Italian physicist Enrico Fermi, which is also the story of thirty years that transformed physics and forever changed our understanding of matter and the universe: nuclear physics and elementary particle physics were born, nuclear fission was discovered, the Manhattan Project was developed, the atomic bombs were dropped, and the era of “big sc…
The discovery of a virtual turning point truly is a breakthrough in WKB analysis of higher order differential equations. This monograph expounds the core part of its theory together with its application to the analysis of higher order Painlevé equations of the Noumi–Yamada type and to the analysis of non-adiabatic transition probability problems in three levels. As M.V. Fedoryuk once lame…
From the central concept of the field—which depicts the world as a mutually interactive whole, with each part connected to every other part by an underlying field— have come models as diverse as quantum mathematics and Saussure’s theory of language. In The Cosmic Web, N. Katherine Hayles seeks to establish the scope of the field concept and to assess its importance for contemporary though…
This is a book about the Hilbert space formulation of quantum mechanics and its measurement theory. It contains a synopsis of what became of the Mathematical Foundations of Quantum Mechanics since von Neumann’s classic treatise with this title. Fundamental non-classical features of quantum mechanics—indeterminacy and incompatibility of observables, unavoidable measurement disturbance, entan…
This book tells the fascinating story of the people and events behind the turbulent changes in attitudes to quantum theory in the second half of the 20th century. The huge success of quantum mechanics as a predictive theory has been accompanied, from the very beginning, by doubts and controversy about its foundations and interpretation. This book looks in detail at how research on foundations e…
This book describes a relativistic quantum theory developed by the author starting from the E.C.G. Stueckelberg approach proposed in the early 40s. In this framework a universal invariant evolution parameter (corresponding to the time originally postulated by Newton) is introduced to describe dynamical evolution. This theory is able to provide solutions for some of the fundamental problems enco…
This thesis addresses the intriguing topic of the quantum tunnelling of many-body systems such as Bose-Einstein condensates. Despite the enormous amount of work on the tunneling of a single particle through a barrier, we know very little about how a system made of several or of many particles tunnels through a barrier to open space. The present work uses numerically exact solutions of the time-…
This book provides readers with a concise introduction to current studies on operator-algebras and their generalizations, operator spaces and operator systems, with a special focus on their application in quantum information science. This basic framework for the mathematical formulation of quantum information can be traced back to the mathematical work of John von Neumann, one of the pioneers o…
These lecture notes present a concise and introductory, yet as far as possible coherent, view of the main formalizations of quantum mechanics and of quantum field theories, their interrelations and their theoretical foundations. The “standard” formulation of quantum mechanics (involving the Hilbert space of pure states, self-adjoint operators as physical observables, and the probabilisti…