A Second Course In Topos Quantum Theory

DOWNLOAD

Download A Second Course In Topos Quantum Theory PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get A Second Course In Topos Quantum Theory 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

A Second Course In Topos Quantum Theory

DOWNLOAD
Author : Cecilia Flori
language : en
Publisher: Springer
Release Date : 2018-02-08

A Second Course In Topos Quantum Theory written by Cecilia Flori and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-08 with Science categories.

This advanced course, a sequel to the first volume of this lecture series on topos quantum theory, delves deeper into the theory, addressing further technical aspects and recent advances. These include, but are not limited to, the development of physical quantities and self-adjoint operators; insights into the quantization process; the description of an alternative, covariant version of topos quantum theory; and last but not least, the development of a new concept of spacetime. The book builds on the concepts introduced in the first volume (published as Lect. Notes Phys. 868), which presents the main building blocks of the theory and how it could provide solutions to interpretational problems in quantum theory, such as: What are the main conceptual issues in quantum theory? And how can these issues be solved within a new theoretical framework of quantum theory? These two volumes together provide a complete, basic course on topos quantum theory, offering a set of mathematical tools to readers interested in tackling fundamental issues in quantum theory in general, and in quantum gravity in particular. From the reviews of the first volume: The book is self-contained and can be used as a textbook or self-study manual teaching the usage of category theory and topos theory, in particular in theoretical physics or in investigating the foundations of quantum theory in mathematically rigorous terms. [The] book is a very welcome contribution. Frank Antonsen, Mathematical Reviews, December, 2013

A First Course In Topos Quantum Theory

DOWNLOAD
Author : Cecilia Flori
language : en
Publisher: Springer
Release Date : 2013-03-27

A First Course In Topos Quantum Theory written by Cecilia Flori and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-27 with Science categories.

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 fundamental issues may need to be solved before attempting to define a quantum theory of gravity. The present text adopts this point of view, addressing the following basic questions: What are the main conceptual issues in quantum theory? How can these issues be solved within a new theoretical framework of quantum theory? A possible way to overcome critical issues in present-day quantum physics – such as a priori assumptions about space and time that are not compatible with a theory of quantum gravity, and the impossibility of talking about systems without reference to an external observer – is through a reformulation of quantum theory in terms of a different mathematical framework called topos theory. This course-tested primer sets out to explain to graduate students and newcomers to the field alike, the reasons for choosing topos theory to resolve the above-mentioned issues and how it brings quantum physics back to looking more like a “neo-realist” classical physics theory again.

New Structures For Physics

DOWNLOAD
Author : Bob Coecke
language : en
Publisher: Springer Science & Business Media
Release Date : 2011

New Structures For Physics written by Bob Coecke 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 with Computers categories.

This volume provides a series of tutorials on mathematical structures which recently have gained prominence in physics, ranging from quantum foundations, via quantum information, to quantum gravity. These include the theory of monoidal categories and corresponding graphical calculi, Girard’s linear logic, Scott domains, lambda calculus and corresponding logics for typing, topos theory, and more general process structures. Most of these structures are very prominent in computer science; the chapters here are tailored towards an audience of physicists.

Reality And Measurement In Algebraic Quantum Theory

DOWNLOAD
Author : Masanao Ozawa
language : en
Publisher: Springer
Release Date : 2018-11-02

Reality And Measurement In Algebraic Quantum Theory written by Masanao Ozawa and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-02 with Mathematics categories.

This volume contains papers based on presentations at the “Nagoya Winter Workshop 2015: Reality and Measurement in Algebraic Quantum Theory (NWW 2015)”, held in Nagoya, Japan, in March 2015. The foundations of quantum theory have been a source of mysteries, puzzles, and confusions, and have encouraged innovations in mathematical languages to describe, analyze, and delineate this wonderland. Both ontological and epistemological questions about quantum reality and measurement have been placed in the center of the mysteries explored originally by Bohr, Heisenberg, Einstein, and Schrödinger. This volume describes how those traditional problems are nowadays explored from the most advanced perspectives. It includes new research results in quantum information theory, quantum measurement theory, information thermodynamics, operator algebraic and category theoretical foundations of quantum theory, and the interplay between experimental and theoretical investigations on the uncertainty principle. This book is suitable for a broad audience of mathematicians, theoretical and experimental physicists, and philosophers of science.

Lectures On Field Theory And Topology

DOWNLOAD
Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-23

Lectures On Field Theory And Topology written by Daniel S. Freed 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 2019-08-23 with Mathematics categories.

These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.

Foundations Of Quantum Theory

DOWNLOAD
Author : Klaas Landsman
language : en
Publisher: Springer
Release Date : 2017-05-11

Foundations Of Quantum Theory written by Klaas Landsman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-05-11 with Science categories.

This book studies the foundations of quantum theory through its relationship to classical physics. This idea goes back to the Copenhagen Interpretation (in the original version due to Bohr and Heisenberg), which the author relates to the mathematical formalism of operator algebras originally created by von Neumann. The book therefore includes comprehensive appendices on functional analysis and C*-algebras, as well as a briefer one on logic, category theory, and topos theory. Matters of foundational as well as mathematical interest that are covered in detail include symmetry (and its "spontaneous" breaking), the measurement problem, the Kochen-Specker, Free Will, and Bell Theorems, the Kadison-Singer conjecture, quantization, indistinguishable particles, the quantum theory of large systems, and quantum logic, the latter in connection with the topos approach to quantum theory. This book is Open Access under a CC BY licence.

Theories Sites Toposes

DOWNLOAD
Author : Olivia Caramello
language : en
Publisher: Oxford University Press
Release Date : 2018

Theories Sites Toposes written by Olivia Caramello and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018 with Mathematics categories.

According to Grothendieck, the notion of topos is "the bed or deep river where come to be married geometry and algebra, topology and arithmetic, mathematical logic and category theory, the world of the continuous and that of discontinuous or discrete structures". It is what he had "conceived of most broad to perceive with finesse, by the same language rich of geometric resonances, an "essence" which is common to situations most distant from each other, coming from one region or another of the vast universe of mathematical things". The aim of this book is to present a theory and a number of techniques which allow to give substance to Grothendieck's vision by building on the notion of classifying topos educed by categorical logicians. Mathematical theories (formalized within first-order logic) give rise to geometric objects called sites; the passage from sites to their associated toposes embodies the passage from the logical presentation of theories to their mathematical content, i.e. from syntax to semantics. The essential ambiguity given by the fact that any topos is associated in general with an infinite number of theories or different sites allows to study the relations between different theories, and hence the theories themselves, by using toposes as 'bridges' between these different presentations. The expression or calculation of invariants of toposes in terms of the theories associated with them or their sites of definition generates a great number of results and notions varying according to the different types of presentation, giving rise to a veritable mathematical morphogenesis.

Three Roads To Quantum Gravity

DOWNLOAD
Author : Lee Smolin
language : en
Publisher: Hachette UK
Release Date : 2014-03-20

Three Roads To Quantum Gravity written by Lee Smolin and has been published by Hachette UK this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-20 with Science categories.

A leading theoretical physicist describes the search for a 'theory of everything'. The Holy Grail of modern physics is the search for a 'quantum gravity' view of the universe that unites Einstein's general relativity with quantum theory. Until recently, these two foundational pillars of modern science have seemed incompatible: relativity deals exclusively with the universe at the large scale (planets, solar systems and galaxies), whereas quantum theory is restricted to the domain of the very small (molecules, atoms, electrons). Here, Lee Smolin provides the first accessible overview of current attempts to reconcile these two theories. Written with wit and style, Three Roads to Quantum Gravity touches on some of the deepest questions about the nature of the universe - are space and time continuous or infinitely divisible? Is there a limit to how small things can be? - while speculating on what developments we can expect at the frontiers of physics in the twenty-first century.

Deep Beauty

DOWNLOAD
Author : Hans Halvorson
language : en
Publisher: Cambridge University Press
Release Date : 2011-04-18

Deep Beauty written by Hans Halvorson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-18 with Mathematics categories.

No scientific theory has caused more puzzlement and confusion than quantum theory. Physics is supposed to help us to understand the world, but quantum theory makes it seem a very strange place. This book is about how mathematical innovation can help us gain deeper insight into the structure of the physical world. Chapters by top researchers in the mathematical foundations of physics explore new ideas, especially novel mathematical concepts at the cutting edge of future physics. These creative developments in mathematics may catalyze the advances that enable us to understand our current physical theories, especially quantum theory. The authors bring diverse perspectives, unified only by the attempt to introduce fresh concepts that will open up new vistas in our understanding of future physics.

Collected Papers Of Salomon Bochner

DOWNLOAD
Author : Salomon Bochner
language : en
Publisher: American Mathematical Soc.
Release Date : 1992

Collected Papers Of Salomon Bochner written by Salomon Bochner 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 1992 with Mathematics categories.

Collected papers of Salomon Bochner, American mathematician, known for work in mathematical analysis, probability theory and differential geometry.