These notes investigate the time evolution of quantum systems, and in particular the rigorous derivation of effective equations approximating the many-body Schrödinger dynamics in certain physically interesting regimes. The focus is primarily on the derivation of time-dependent effective theories (non-equilibrium question) approximating many-body quantum dynamics. The book is divided into seven sections, the first of which briefly reviews the main properties of many-body quantum systems an...

Although ideas from quantum physics play an important role in many parts of modern mathematics, there are few books about quantum mechanics aimed at mathematicians. This book introduces the main ideas of quantum mechanics in language familiar to mathematicians. Readers with little prior exposure to physics will enjoy the book's conversational tone as they delve into such topics as the Hilbert space approach to quantum theory; the Schrödinger equation in one space dimension; the Spectral Th...

Quirky Quantum Concepts explains the more important and more difficult concepts in theoretical quantum mechanics, especially those which are consistently neglected or confusing in many common expositions. The emphasis is on physical understanding, which is necessary for the development of new, cutting edge science.In particular, this book explains the basis for many standard quantum methods, which are too often presented without sufficient motivation or interpretation. The...

Our understanding of the physical universe underwent a revolution in the early twentieth century - evolving from the classical physics of Newton, Galileo, and Maxwell to the modern physics of relativity and quantum mechanics. The dominant figure in this revolutionary change was Albert Einstein. In a single year, 1905, Einstein produced breakthrough works in three areas of physics: on the size and the effects of atoms; on the quantization of the electromagnetic field; and on the special the...

In this third volume of The Quantum Theory of Fields, available for the first time in paperback, Nobel Laureate Steven Weinberg continues his masterly exposition of quantum field theory. This volume presents a self-contained, up-to-date and comprehensive introduction to supersymmetry, a highly active area of theoretical physics. The text introduces and explains a broad range of topics, including supersymmetric algebras, supersymmetric field theories, extended supersymmetry, supergraphs, no...

The topics of this book are the mathematical foundations of non-relativistic quantum mechanics and the mathematical theory they require. The main characteristic of the book is that the mathematics is developed assuming familiarity with elementary analysis only. Moreover, all the proofs are carried out in detail. These features make the book easily accessible to readers with only the mathematical training offered by undergraduate education in mathematics or in physics, and also ideal for in...

Quantum field theory is the basic mathematical framework that is used to describe elementary particles. This textbook provides a complete and essential introduction to the subject. Assuming only an undergraduate knowledge of quantum mechanics and special relativity, this book is ideal for graduate students beginning the study of elementary particles. The step-by-step presentation begins with basic concepts illustrated by simple examples, and proceeds through historically important results ...

In this thesis, quantum estimation theory is applied to investigate uncertainty relations between error and disturbance in quantum measurement. The author argues that the best solution for clarifying the attainable bound of the error and disturbance is to invoke the estimation process from the measurement outcomes such as signals from a photodetector in a quantum optical system. The error and disturbance in terms of the Fisher information content have been successfully formulated and provi...

In physics, the idea of extra spatial dimensions originates from Nordstöm’s 5-dimensional vector theory in 1914, followed by Kaluza-Klein theory in 1921, in an effort to unify general relativity and electromagnetism in a 5 dimensional space-time (4 dimensions for space and 1 for time). Kaluza–Klein theory didn’t generate enough interest with physicist for the next five decades, due to its problems with inconsistencies. With the advent of supergravity theory (the theory that unifies general...

This book is a collection of lecture notes and contributions in “Summer School on Diversities in Quantum Computation/Information” held on 1-5 August, 2010 at U-Community Hotel, Higashi-Osaka, Japan. Lecturers are world class authorities in respective areas in quantum information and quantum computing including physics, mathematics, chemistry and information science. They lectured on cutting-edge research frontiers where they are currently working, including quantum error correction, relati...

In the last five decades various attempts to formulate theories of quantum gravity have been made, but none has fully succeeded in becoming the quantum theory of gravity. One possible explanation for this failure might be the unresolved fundamental issues in quantum theory as it stands now. Indeed, most approaches to quantum gravity adopt standard quantum theory as their starting point, with the hope that the theory’s unresolved issues will get solved along the way. However, these...

In this volume the fundamental theory of open quantum systems is revised in the light of modern developments in the field. A unified approach to the quantum evolution of open systems is presented by merging concepts and methods traditionally employed by different communities, such as quantum optics, condensed matter, chemical physics and mathematical physics.The mathematical structure and the general properties of the dynamical maps underlying open system dynamics are explained in d...