* Which problems do arise within relativistic enhancements of the Schrodinger theory, especially if one adheres to the usual one-particle interpretation? * To what extent can these problems be overcome? * What is the physical necessity of quantum field theories? In many textbooks, only insufficient answers to these fundamental questions are provided by treating the relativistic quantum mechanical one-particle concept very superficially and instead introducing field quantization as soon as possible. By contrast, this book emphasizes particularly this point of view (relativistic quantum...
* Which problems do arise within relativistic enhancements of the Schrodinger theory, especially if one adheres to the usual one-particle interpretati...
This book offers a modern way of dealing with the problems of equilibrium states of Bose systems. Starting with the variation principle of statistical mechanics and the energy-entropy balance principle as equilibrium criteria, results for general boson systems and models are explicitly derived using simple functional analytic calculus.
Bridging the gap between general theoretical physics and the phenomenological research in the field of Bose systems, this book provides an insight into the fascinating quantum world of bosons. Key topics include the occurrence of BEC and its intimate...
This book offers a modern way of dealing with the problems of equilibrium states of Bose systems. Starting with the variation principle of statisti...
The main aim of this book is to develop the methods of Global Analysis and of Stochastic Analysis such that their combination allows one to have a more or less common treatment for areas of mathematical physics that traditionally are considered as quite distant from each other and requiring different methods of investigation. Among those areas we mention classical mechanics on non-linear configuration spaces, some problems of statistical and quantum physics, hydrodynamics, etc. The idea, yielding the unification of these topics, is based on the use of a geometrically invariant form of...
The main aim of this book is to develop the methods of Global Analysis and of Stochastic Analysis such that their combination allows one to have a ...
This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum field theory. All methods are illustrated with applications to specific physical problems from the forefront of current research, such as finite-temperature field theory, D-branes, quantum solitons and noncommutativity. In the first part of the book, necessary background information on differential geometry and quantization, including less standard material, is collected. The second part of the book contains a detailed description of main spectral...
This book gives a detailed and self-contained introduction into the theory of spectral functions, with an emphasis on their applications to quantum fi...
Density Functional Theory (DFT) has firmly established itself as the workhorse for atomic-level simulations of condensed phases, pure or composite materials and quantum chemical systems. This work offers a rigorous and detailed introduction to the foundations of this theory, up to and including such advanced topics as orbital-dependent functionals as well as both time-dependent and relativistic DFT. Given the many ramifications of contemporary DFT, the text concentrates on the self-contained presentation of the basics of the most widely used DFT variants: this implies a thorough discussion of...
Density Functional Theory (DFT) has firmly established itself as the workhorse for atomic-level simulations of condensed phases, pure or composite mat...
This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems including nano and bio systems.
It includes introductory material on algorithm, functional analysis, probability theory, information theory, quantum mechanics and quantum field theory. Apart from standard material on quantum information like quantum algorithm and teleportation, the authors discuss findings on the theory of entropy in C*-dynamical systems, space-time dependence of quantum entangled states, entangling operators, adaptive...
This monograph provides a mathematical foundation to the theory of quantum information and computation, with applications to various open systems i...
This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherent states, wavelets, and some of their generalizations, it emphasizes mathematical principles, subsuming the theories of both wavelets...
This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear ...
Simple random walks - or equivalently, sums of independent random vari- ables - have long been a standard topic of probability theory and mathemat- ical physics. In the 1950s, non-Markovian random-walk models, such as the self-avoiding walk,were introduced into theoretical polymer physics, and gradu- ally came to serve as a paradigm for the general theory of critical phenomena. In the past decade, random-walk expansions have evolved into an important tool for the rigorous analysis of critical phenomena in classical spin systems and of the continuum limit in quantum field theory. Among the...
Simple random walks - or equivalently, sums of independent random vari- ables - have long been a standard topic of probability theory and mathemat- ic...
In this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, presents a timely analysis of theoretical physics and related fundamental problems.
In this highly readable book, H.S. Green, a former student of Max Born and well known as an author in physics and in the philosophy of science, pre...
This book is devoted to some recently developed techniques in quantum field theory (QFT), as well as to their main applications to different areas of parti cle physics. All together they are known as the effective or phenomenological Lagrangian formalism. Motivated by the enormous amount of work carried out in this field during the last years, our purpose when writing this book has been to give a modern and pedagogical exposition of the most relevant as pects of the topic. We hope that our efforts will be useful, both for graduated students in the search for a solid theoretical background in...
This book is devoted to some recently developed techniques in quantum field theory (QFT), as well as to their main applications to different areas of ...
