Download or read book Entanglement Measures and Their Properties in Quantum Field Theory written by Stefan Hollands and published by Springer. This book was released on 2018-10-12 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigorous treatment of entanglement measures in the general context of quantum field theory. It covers a broad range of models and the use of fields allows us to properly take the localization of systems into account. The required mathematical techniques are introduced in a self-contained way.
Download or read book Progress and Visions in Quantum Theory in View of Gravity written by Felix Finster and published by Springer Nature. This book was released on 2020-04-09 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a critical discussion of the status and prospects of current approaches in quantum mechanics and quantum field theory, in particular concerning gravity. It contains a carefully selected cross-section of lectures and discussions at the seventh conference “Progress and Visions in Quantum Theory in View of Gravity” which took place in fall 2018 at the Max Planck Institute for Mathematics in the Sciences in Leipzig. In contrast to usual proceeding volumes, instead of reporting on the most recent technical results, contributors were asked to discuss visions and new ideas in foundational physics, in particular concerning foundations of quantum field theory. A special focus has been put on the question of which physical principles of quantum (field) theory can be considered fundamental in view of gravity. 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.
Download or read book Frontiers in Quantum Information Research written by Mikio Nakahara and published by World Scientific. This book was released on 2012 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Selected Topics on the General Properties of Quantum Field Theory written by F. Strocchi and published by World Scientific. This book was released on 1993 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a readable account of the foundations of QFT, in particular of the Euclidean formulation with emphasis on the interplay between physical requirements and mathematical structures. The general structures underlying the conventional local (renormalizable) formulation of gauge QFT are discussed also on the basis of simple models. The mechanism of confinement, non-trivial topology and ?-vacua, chiral symmetry breaking and solution of the U(1) problem are clarified through a careful analysis of the Schwinger model, which settles unclear or debated points.
Download or read book Field Theories of Condensed Matter Physics written by Eduardo Fradkin and published by Cambridge University Press. This book was released on 2013-02-28 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Presenting the physics of the most challenging problems in condensed matter using the conceptual framework of quantum field theory, this book is of great interest to physicists in condensed matter and high energy and string theorists, as well as mathematicians. Revised and updated, this second edition features new chapters on the renormalization group, the Luttinger liquid, gauge theory, topological fluids, topological insulators and quantum entanglement. The book begins with the basic concepts and tools, developing them gradually to bring readers to the issues currently faced at the frontiers of research, such as topological phases of matter, quantum and classical critical phenomena, quantum Hall effects and superconductors. Other topics covered include one-dimensional strongly correlated systems, quantum ordered and disordered phases, topological structures in condensed matter and in field theory and fractional statistics.
Download or read book Quantum Entanglement in High Energy Physics written by Oliver K. Baker and published by BoD – Books on Demand. This book was released on 2024-04-24 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to research topics in quantum entanglement at the energy frontier of particle and nuclear physics, and important interdisciplinary collaborations with colleagues from fields outside of physics. A non-exhaustive list of examples of the latter can include mathematics, computer science, social sciences, philosophy, and how physics can interact with them in a way that supports successful outcomes. These are exciting times in the field of quantum information science, with new research results and their applications in society exhibiting themselves rather frequently. But what is even more exciting is that the frequency of these new results and their applications increases with a rapidity that will motivate new methods, new theories, new experiments, and new collaborations outside of the field that future researchers will find quite challenging.
Download or read book Entanglement Between Noncomplementary Parts of Many Body Systems written by Hannu Christian Wichterich and published by Springer Science & Business Media. This book was released on 2011-05-18 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis investigates the structure and behaviour of entanglement, the purely quantum mechanical part of correlations, in many-body systems, employing both numerical and analytical techniques at the interface of condensed matter theory and quantum information theory. Entanglement can be seen as a precious resource which, for example, enables the noiseless and instant transmission of quantum information, provided the communicating parties share a sufficient "amount" of it. Furthermore, measures of entanglement of a quantum mechanical state are perceived as useful probes of collective properties of many-body systems. For instance, certain measures are capable of detecting and classifying ground-state phases and, particularly, transition (or critical) points separating such phases. Chapters 2 and 3 focus on entanglement in many-body systems and its use as a potential resource for communication protocols. They address the questions of how a substantial amount of entanglement can be established between distant subsystems, and how efficiently this entanglement could be "harvested" by way of measurements. The subsequent chapters 4 and 5 are devoted to universality of entanglement between large collections of particles undergoing a quantum phase transition, where, despite the enormous complexity of these systems, collective properties including entanglement no longer depend crucially on the microscopic details.
Download or read book Nonlocal Quantum Field Theory and Stochastic Quantum Mechanics written by K.H. Namsrai and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: over this stochastic space-time leads to the non local fields considered by G. V. Efimov. In other words, stochasticity of space-time (after being averaged on a large scale) as a self-memory makes the theory nonlocal. This allows one to consider in a unified way the effect of stochasticity (or nonlocality) in all physical processes. Moreover, the universal character of this hypothesis of space-time at small distances enables us to re-interpret the dynamics of stochastic particles and to study some important problems of the theory of stochastic processes [such as the relativistic description of diffusion, Feynman type processes, and the problem of the origin of self-turbulence in the motion of free particles within nonlinear (stochastic) mechanics]. In this direction our approach (Part II) may be useful in recent developments of the stochastic interpretation of quantum mechanics and fields due to E. Nelson, D. Kershaw, I. Fenyes, F. Guerra, de la Pena-Auerbach, J. -P. Vigier, M. Davidson, and others. In particular, as shown by N. Cufaro Petroni and J. -P. Vigier, within the discussed approach, a causal action-at-distance interpretation of a series of experiments by A. Aspect and his co-workers indicating a possible non locality property of quantum mechanics, may also be obtained. Aspect's results have recently inspired a great interest in different nonlocal theories and models devoted to an understanding of the implications of this nonlocality. This book consists of two parts.
Download or read book Topology and Quantum Theory in Interaction written by David Ayala and published by American Mathematical Soc.. This book was released on 2018-10-25 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NSF-CBMS Regional Conference on Topological and Geometric Methods in QFT, held from July 31–August 4, 2017, at Montana State University in Bozeman, Montana. In recent decades, there has been a movement to axiomatize quantum field theory into a mathematical structure. In a different direction, one can ask to test these axiom systems against physics. Can they be used to rederive known facts about quantum theories or, better yet, be the framework in which to solve open problems? Recently, Freed and Hopkins have provided a solution to a classification problem in condensed matter theory, which is ultimately based on the field theory axioms of Graeme Segal. Papers contained in this volume amplify various aspects of the Freed–Hopkins program, develop some category theory, which lies behind the cobordism hypothesis, the major structure theorem for topological field theories, and relate to Costello's approach to perturbative quantum field theory. Two papers on the latter use this framework to recover fundamental results about some physical theories: two-dimensional sigma-models and the bosonic string. Perhaps it is surprising that such sparse axiom systems encode enough structure to prove important results in physics. These successes can be taken as encouragement that the axiom systems are at least on the right track toward articulating what a quantum field theory is.
Download or read book Holographic Entanglement Entropy written by Mukund Rangamani and published by . This book was released on 2017 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of developments in the field of holographic entanglement entropy. Within the context of the AdS/CFT correspondence, it is shown how quantum entanglement is computed by the area of certain extremal surfaces. The general lessons one can learn from this connection are drawn out for quantum field theories, many-body physics, and quantum gravity. An overview of the necessary background material is provided together with a flavor of the exciting open questions that are currently being discussed. The book is divided into four main parts. In the first part, the concept of entanglement, and methods for computing it, in quantum field theories is reviewed. In the second part, an overview of the AdS/CFT correspondence is given and the holographic entanglement entropy prescription is explained. In the third part, the time-dependence of entanglement entropy in out-of-equilibrium systems, and applications to many body physics are explored using holographic methods. The last part focuses on the connection between entanglement and geometry. Known constraints on the holographic map, as well as, elaboration of entanglement being a fundamental building block of geometry are explained. The book is a useful resource for researchers and graduate students interested in string theory and holography, condensed matter and quantum information, as it tries to connect these different subjects linked by the common theme of quantum entanglement.
Download or read book Geometry of Quantum States written by Ingemar Bengtsson and published by Cambridge University Press. This book was released on 2017-08-18 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum information theory is a branch of science at the frontier of physics, mathematics, and information science, and offers a variety of solutions that are impossible using classical theory. This book provides a detailed introduction to the key concepts used in processing quantum information and reveals that quantum mechanics is a generalisation of classical probability theory. The second edition contains new sections and entirely new chapters: the hot topic of multipartite entanglement; in-depth discussion of the discrete structures in finite dimensional Hilbert space, including unitary operator bases, mutually unbiased bases, symmetric informationally complete generalized measurements, discrete Wigner function, and unitary designs; the Gleason and Kochen–Specker theorems; the proof of the Lieb conjecture; the measure concentration phenomenon; and the Hastings' non-additivity theorem. This richly-illustrated book will be useful to a broad audience of graduates and researchers interested in quantum information theory. Exercises follow each chapter, with hints and answers supplied.
Download or read book The Universal Coefficient Theorem and Quantum Field Theory written by Andrei-Tudor Patrascu and published by Springer. This book was released on 2016-09-23 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis describes a new connection between algebraic geometry, topology, number theory and quantum field theory. It offers a pedagogical introduction to algebraic topology, allowing readers to rapidly develop basic skills, and it also presents original ideas to inspire new research in the quest for dualities. Its ambitious goal is to construct a method based on the universal coefficient theorem for identifying new dualities connecting different domains of quantum field theory. This thesis opens a new area of research in the domain of non-perturbative physics—one in which the use of different coefficient structures in (co)homology may lead to previously unknown connections between different regimes of quantum field theories. The origin of dualities is an issue in fundamental physics that continues to puzzle the research community with unexpected results like the AdS/CFT duality or the ER-EPR conjecture. This thesis analyzes these observations from a novel and original point of view, mainly based on a fundamental connection between number theory and topology. Beyond its scientific qualities, it also offers a pedagogical introduction to advanced mathematics and its connection with physics. This makes it a valuable resource for students in mathematical physics and researchers wanting to gain insights into (co)homology theories with coefficients or the way in which Grothendieck's work may be connected with physics.
Download or read book Quantum Field Theory and the Many body Problem written by Theodore David Schultz and published by CRC Press. This book was released on 1987 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Entanglement Information and the Interpretation of Quantum Mechanics written by Gregg Jaeger and published by Springer Science & Business Media. This book was released on 2009-06-12 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Entanglement was initially thought by some to be an oddity restricted to the realm of thought experiments. However, Bell’s inequality delimiting local - havior and the experimental demonstration of its violation more than 25 years ago made it entirely clear that non-local properties of pure quantum states are more than an intellectual curiosity. Entanglement and non-locality are now understood to ?gure prominently in the microphysical world, a realm into which technology is rapidly hurtling. Information theory is also increasingly recognized by physicists and philosophers as intimately related to the foun- tions of mechanics. The clearest indicator of this relationship is that between quantum information and entanglement. To some degree, a deep relationship between information and mechanics in the quantum context was already there to be seen upon the introduction by Max Born and Wolfgang Pauli of the idea that the essence of pure quantum states lies in their provision of probabilities regarding the behavior of quantum systems, via what has come to be known as the Born rule. The signi?cance of the relationship between mechanics and information became even clearer with Leo Szilard’s analysis of James Clerk Maxwell’s infamous demon thought experiment. Here, in addition to examining both entanglement and quantum infor- tion and their relationship, I endeavor to critically assess the in?uence of the study of these subjects on the interpretation of quantum theory.
Download or read book Scattering in Quantum Field Theories written by Daniel Iagolnitzer and published by Princeton University Press. This book was released on 2014-07-14 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: Axiomatic and constructive approaches to quantum field theory first aim to establish it on precise, non-perturbative bases: general axioms and rigorous definition of specific theories respectively. From the viewpoint of particle physics, the goal is then to develop a relativistic scattering theory, including particle analysis and the derivation of general properties of collision amplitudes. Taking into account successive improvements, this book provides a modern, self-contained, and coherent presentation of important developments from the last twenty years, most of which have not been treated or discussed in detail in earlier books. These developments include in particular the axiomatic derivation, in massive theories, of general causal and momentum-space analyticity properties of multiparticle collision amplitudes; the constructive definition, initially in the (unphysical) euclidean space, of various models including non-super-renormalizable theories treated in the 1980s via phase-space expansions; and the subsequent constructive approach to scattering theory, which provides information on the mass spectrum, asymptotic completeness, and multiparticle structure in increasingly higher energy regions. Originally published in 1993. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Nonperturbative Quantum Field Theory written by G. Hooft and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past 15 years, quantum field theory and classical statistical mechanics have merged into a single field, and the need for nonperturbative methods for the description of critical phenomena in statistical mechanics as well as for problems in elementary particle physics are generally acknowledged. Such methods formed the central theme of the 1987 Cargese Advanced Study Institut. e on "Nonpert. urbat. ive Quantum Field Theory." The use of conformal symmet. ry has been of central interest in recent years, and was a main subject at. t. he ASI. Conformal invariant quantum field theory describes statistical mechanical systems exactly at a critical point, and can be analysed to a remarkable ext. ent. by group t. heoretical methods. Very strong results have been obtained for 2-dimensional systems. Conformal field theory is also the basis of string theory, which offers some hope of providing a unified t. heory of all interactions between elementary particles. Accordingly, a number of lectures and seminars were presented on these two topics. After syst. ematic introductory lectures, conformal field theory on Riemann surfaces, orbifolds, sigma models, and application of loop group theory and Grassmannians were discussed, and some ideas on modular geometry were presented. Other lectures combined' traditional techniques of constructive quant. um field theory with new methods such as the use of index-t. heorems and infinite dimensional (Kac Moody) symmetry groups. The problems encountered in a quantum mechanical description of black holes were discussed in detail.
Download or read book Lectures on General Quantum Correlations and their Applications written by Felipe Fernandes Fanchini and published by Springer. This book was released on 2017-06-24 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a distinctive way of understanding quantum correlations beyond entanglement, introducing readers to this less explored yet very fundamental aspect of quantum theory. It takes into account most of the new ideas involving quantum phenomena, resources, and applications without entanglement, both from a theoretical and an experimental point of view. This book serves as a reference for both beginner students and experienced researchers in physics and applied mathematics, with an interest in joining this novel venture towards understanding the quantum nature of the world.
