Quanta Of Maths
DOWNLOAD
Download Quanta Of Maths PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Quanta Of Maths book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Quanta Of Maths
DOWNLOAD
Author : Institut des hautes études scientifiques (Paris, France)
language : en
Publisher: American Mathematical Soc.
Release Date : 2010
Quanta Of Maths written by Institut des hautes études scientifiques (Paris, France) and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
The work of Alain Connes has cut a wide swath across several areas of mathematics and physics. Reflecting its broad spectrum and profound impact on the contemporary mathematical landscape, this collection of articles covers a wealth of topics at the forefront of research in operator algebras, analysis, noncommutative geometry, topology, number theory and physics. Specific themes covered by the articles are as follows: entropy in operator algebras, regular $C^*$-algebras of integral domains, properly infinite $C^*$-algebras, representations of free groups and 1-cohomology, Leibniz seminorms and quantum metric spaces; von Neumann algebras, fundamental Group of $\mathrm{II}_1$ factors, subfactors and planar algebras; Baum-Connes conjecture and property T, equivariant K-homology, Hermitian K-theory; cyclic cohomology, local index formula and twisted spectral triples, tangent groupoid and the index theorem; noncommutative geometry and space-time, spectral action principle, quantum gravity, noncommutative ADHM and instantons, non-compact spectral triples of finite volume, noncommutative coordinate algebras; Hopf algebras, Vinberg algebras, renormalization and combinatorics, motivic renormalization and singularities; cyclotomy and analytic geometry over $F_1$, quantum modular forms; differential K-theory, cyclic theory and S-cohomology.
Quanta Logic And Spacetime
DOWNLOAD
Author : Stephen Allan Selesnick
language : en
Publisher: World Scientific
Release Date : 2003
Quanta Logic And Spacetime written by Stephen Allan Selesnick and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.
In this expanded edition of Quanta, Logic and Spacetime, the logical base is greatly broadened and quantum-computational aspects of the approach are brought to the fore. The first two parts of this edition may indeed be regarded as providing a self-contained and logic-based foundation for ? and an introduction to ? the enterprise known as quantum computing.The rest of the work takes on the task (as in the first edition) of computing from first principles certain dynamical expressions which turn out to compare favorably with the Lagrangian densities of the (massless) Standard Model, including gravity. The logic of this process is now subject to greater formal rigor than was possible in the first edition, and the central thesis ? that quantum physics at a fundamental level may itself be realized as a species of quantum computation ? is strongly underscored.
Quanta Logic And Spacetime Variations On Finkelstein S Quantum Relativity
DOWNLOAD
Author : Selesnick Steve A
language : en
Publisher: World Scientific
Release Date : 1998-03-12
Quanta Logic And Spacetime Variations On Finkelstein S Quantum Relativity written by Selesnick Steve A and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-03-12 with Science categories.
In this highly interesting monograph, a brief account of Finkelstein's approach to quantum theory and some of its ramifications is given. Specifically, his suggestion that some sort of quantum-set-like structure should underlie our macroscopic perception of spacetime is developed to the point where a fair slice of fundamental physics (for a massless world) may be formally derived in an elementary fashion from the ground up. In detail, a model of what Finkelstein has dubbed a “quantum net”, in conjunction with a carefully and extensively articulated correspondence principle, gives rise to the standard Lagrangians for: massless Dirac fermions, general relativity, and Yang-Mills fields for the gauge groups, U(1) x SU(2), and SU(3). These Lagrangians emerge replete with (Feynman) gauge-fixing terms and ghost fields, and a chiral breaking mechanism in the case of SU(2). The results are interpreted in the light of the Standard Model.
The Prime Number Conspiracy
DOWNLOAD
Author : Thomas Lin
language : en
Publisher: MIT Press
Release Date : 2018-12-04
The Prime Number Conspiracy written by Thomas Lin and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-12-04 with Mathematics categories.
Quanta Magazine's stories of mathematical explorations show that “inspiration strikes willy-nilly,” revealing surprising solutions and exciting discoveries. If you're a science and data nerd like me, you may be interested in "Alice and Bob Meet the Wall of Fire" and "The Prime Number Conspiracy" from Quanta Magazine and Thomas Lin. - Bill Gates These stories from Quanta Magazine map the routes of mathematical exploration, showing readers how cutting-edge research is done, while illuminating the productive tension between conjecture and proof, theory and intuition. The stories show that, as James Gleick puts it in the foreword, “inspiration strikes willy-nilly.” One researcher thinks of quantum chaotic systems at a bus stop; another suddenly realizes a path to proving a theorem of number theory while in a friend's backyard; a statistician has a “bathroom sink epiphany” and discovers the key to solving the Gaussian correlation inequality. Readers of The Prime Number Conspiracy, says Quanta editor-in-chief Thomas Lin, are headed on “breathtaking intellectual journeys to the bleeding edge of discovery strapped to the narrative rocket of humanity's never-ending pursuit of knowledge.” Quanta is the only popular publication that offers in-depth coverage of the latest breakthroughs in understanding our mathematical universe. It communicates mathematics by taking it seriously, wrestling with difficult concepts and clearly explaining them in a way that speaks to our innate curiosity about our world and ourselves. Readers of this volume will learn that prime numbers have decided preferences about the final digits of the primes that immediately follow them (the “conspiracy” of the title); consider whether math is the universal language of nature (allowing for “a unified theory of randomness”); discover surprising solutions (including a pentagon tiling proof that solves a century-old math problem); ponder the limits of computation; measure infinity; and explore the eternal question “Is mathematics good for you?” Contributors Ariel Bleicher, Robbert Dijkgraaf, Kevin Hartnett, Erica Klarreich, Thomas Lin, John Pavlus, Siobhan Roberts, Natalie Wolchover Copublished with Quanta Magazine
Light After Dark Iii
DOWNLOAD
Author : Charles Francis
language : en
Publisher: Troubador Publishing Ltd
Release Date : 2016-09-19
Light After Dark Iii written by Charles Francis and has been published by Troubador Publishing Ltd this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-19 with Science categories.
Light after Dark III: The Mathematics of Gravity and Quanta proves the most important results described in Light after Dark II, from fundamental principles, as elegantly as possible and with the minimum of verbiage. This is a first principles account of the mathematical structure of modern theoretical physics, showing that it is not just a disparate bunch of algorithms and procedures, but is a unified structure based on observation, sound principles and solid logic, and allowing a unique physical interpretation in terms of fundamental constituents, or particles. Light after Dark III: The Mathematics of Gravity and Quanta explains essential mathematics at undergraduate level. Part I covers many core topics in a mathematics degree. Part II is a concise account of results in relativity, including the Lorentz transform from first principles, Riemann curvature, Einstein’s equation, derivations of the Schwarzschild and Friedmann solutions, and proofs of key results. Part III contains the mathematical foundations of relativistic quantum mechanics and constructs quantum electrodynamics. Divergence problems are treated with greater rigour than usual in theoretical physics, but without excessive formality. Classical electromagnetism is derived from fundamental principles. Part IV shows how quantum electrodynamics and general relativity can be described in a single structure. Light after Dark III: The Mathematics of Gravity and Quanta will interest students of mathematics and students of physics and philosophy with a mathematical leaning who are seeking a rigorous treatment and deeper mathematical insight into physical theory.
Quantum Mathematics I
DOWNLOAD
Author : Michele Correggi
language : en
Publisher: Springer Nature
Release Date : 2023-12-01
Quantum Mathematics I written by Michele Correggi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-12-01 with Science categories.
This book is the first volume that provides an unique overview of the most recent and relevant contributions in the field of mathematical physics with a focus on the mathematical features of quantum mechanics. It is a collection of review papers together with brand new works related to the activities of the INdAM Intensive Period "INdAM Quantum Meetings (IQM22)", which took place at the Politecnico di Milano in Spring 2022 at Politecnico di Milano. The range of topics covered by the book is wide, going ranging from many-body quantum mechanics to semiclassical analysis, quantum field theory, Schrödinger and Dirac operators and open quantum systems
Mathematical Foundations Of Quantum Theory
DOWNLOAD
Author : A.R. Marlow
language : en
Publisher: Elsevier
Release Date : 2012-12-02
Mathematical Foundations Of Quantum Theory written by A.R. Marlow and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-02 with Science categories.
Mathematical Foundations of Quantum Theory is a collection of papers presented at the 1977 conference on the Mathematical Foundations of Quantum Theory, held in New Orleans. The contributors present their topics from a wide variety of backgrounds and specialization, but all shared a common interest in answering quantum issues. Organized into 20 chapters, this book's opening chapters establish a sound mathematical basis for quantum theory and a mode of observation in the double slit experiment. This book then describes the Lorentz particle system and other mathematical structures with which fundamental quantum theory must deal, and then some unsolved problems in the quantum logic approach to the foundations of quantum mechanics are considered. Considerable chapters cover topics on manuals and logics for quantum mechanics. This book also examines the problems in quantum logic, and then presents examples of their interpretation and relevance to nonclassical logic and statistics. The accommodation of conventional Fermi-Dirac and Bose-Einstein statistics in quantum mechanics or quantum field theory is illustrated. The final chapters of the book present a system of axioms for nonrelativistic quantum mechanics, with particular emphasis on the role of density operators as states. Specific connections of this theory with other formulations of quantum theory are also considered. These chapters also deal with the determination of the state of an elementary quantum mechanical system by the associated position and momentum distribution. This book is of value to physicists, mathematicians, and researchers who are interested in quantum theory.
Operators Geometry And Quanta
DOWNLOAD
Author : Dmitri Fursaev
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-25
Operators Geometry And Quanta written by Dmitri Fursaev and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-25 with Science categories.
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 functions and methods of their calculation. In the third part, the theory is applied to several examples (D-branes, quantum solitons, anomalies, noncommutativity). This book addresses advanced graduate students and researchers in mathematical physics with basic knowledge of quantum field theory and differential geometry. The aim is to prepare readers to use spectral functions in their own research, in particular in relation to heat kernels and zeta functions.
An Introduction To The Mathematical Structure Of Quantum Mechanics
DOWNLOAD
Author : F Strocchi
language : en
Publisher: World Scientific Publishing Company
Release Date : 2008-10-30
An Introduction To The Mathematical Structure Of Quantum Mechanics written by F Strocchi and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-30 with Science categories.
The second printing contains a critical discussion of Dirac derivation of canonical quantization, which is instead deduced from general geometric structures. This book arises out of the need for Quantum Mechanics (QM) to be part of the common education of mathematics students. The mathematical structure of QM is formulated in terms of the C*-algebra of observables, which is argued on the basis of the operational definition of measurements and the duality between states and observables, for a general physical system. The Dirac–von Neumann axioms are then derived. The description of states and observables as Hilbert space vectors and operators follows from the GNS and Gelfand–Naimark Theorems. The experimental existence of complementary observables for atomic systems is shown to imply the noncommutativity of the observable algebra, the distinctive feature of QM; for finite degrees of freedom, the Weyl algebra codifies the experimental complementarity of position and momentum (Heisenberg commutation relations) and Schrödinger QM follows from the von Neumann uniqueness theorem. The existence problem of the dynamics is related to the self-adjointness of the Hamiltonian and solved by the Kato–Rellich conditions on the potential, which also guarantee quantum stability for classically unbounded-below Hamiltonians. Examples are discussed which include the explanation of the discreteness of the atomic spectra. Because of the increasing interest in the relation between QM and stochastic processes, a final chapter is devoted to the functional integral approach (Feynman–Kac formula), to the formulation in terms of ground state correlations (the quantum mechanical analog of the Wightman functions) and their analytic continuation to imaginary time (Euclidean QM). The quantum particle on a circle is discussed in detail, as an example of the interplay between topology and functional integral, leading to the emergence of superselection rules and θ sectors. Errata(s) Errata
Geometry Of Quantum Theory
DOWNLOAD
Author : V.S. Varadarajan
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-03
Geometry Of Quantum Theory written by V.S. Varadarajan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-12-03 with Science categories.
Available for the first time in soft cover, this book is a classic on the foundations of quantum theory. It examines the subject from a point of view that goes back to Heisenberg and Dirac and whose definitive mathematical formulation is due to von Neumann. This view leads most naturally to the fundamental questions that are at the basis of all attempts to understand the world of atomic and subatomic particles.
