Non commutative Geometry

This book provides a systematic, comprehensive and up-to-date account of the recent developments in non-commutative geometry, at a pedagogical level.

Author: Supriya Kar

Publisher: World Scientific Publishing Company Incorporated

ISBN: 9812380523

Category: Mathematics

Page: 250

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This book provides a systematic, comprehensive and up-to-date account of the recent developments in non-commutative geometry, at a pedagogical level. It does not go into the details of rigorous (advanced level) mathematical formulation of non-commutative geometry; rather, it restricts itself to the domain of strings and quantum fields.Since non-commutative geometry has recently aroused renewed interest in open string theory, the author motivates the text from the viewpoint of a string theory. He begins with an introduction to the subject, explaining what one means by non-commutative geometry and why it is relevant to study such geometry, and discussing its possible origin in a string theory.The book comprises nine chapters. Chapter 1 gives a sound mathematical ntroduction to non-commutative spacetime coordinates in classical and quantum physics. In Chapter 2, non-commutativity in a string theory is discussed at a pedagogic level. Chapter 3 deals with an aribitrary D-brane dynamics and Chapter 4 describes the non-commutative gauge theories on a D-brane. In Chapters 5-9, non-commutative quantum field theory (NCQFT) is addressed. In particular, Chapter 5 deals with the real scalar NCQFT, Chapter 6 with that of complex scalar field, Chapter 7 describes spontaneous symmetry breaking in scalar NCQFT, Chapter 8 deals with the U(1) Gauge theory and Chapter 9 with SU(n) Gauge theories.Students will find this book useful as a bridge between string and field theories. In addition, it will prove invaluable for interdisciplinary areas of study.

Noncommutative Geometry And Physics 4 Workshop On Strings Membranes And Topological Field Theory

Phys. 128, 1001 (2012). 3. E. Witten, “Noncommutative Geometry and String Field Theory,” Nucl. Phys. B 268, 253 (1986). 4. T. Erler, “Relating Berkovits and A∞ superstring field theories; small Hilbert space perspective,” JHEP 1510, ...

Author: Kotani Motoko

Publisher: World Scientific

ISBN: 9789813144620

Category: Mathematics

Page: 412

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This book is a collection of the lectures and talks presented in the Tohoku Forum for Creativity in the thematic year 2015 "Fundamental Problems in Quantum Physics: Strings, Black Holes and Quantum Information", and related events in the period 2014–2016. This volume especially contains an overview of recent developments in the theory of strings and membranes, as well as topological field theory.

The Emergence of Spacetime in String Theory

Rather, the angle from which I make my inquiry is given by non-commutative geometry. ... the causal structure of quantum string theory?1 I start considering the issue of causality in the perspective of noncommutative field theories.

Author: Tiziana Vistarini

Publisher: Routledge

ISBN: 9781134842339

Category: Philosophy

Page: 142

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The nature of space and time is one of the most fascinating and fundamental philosophical issues which presently engages at the deepest level with physics. During the last thirty years this notion has been object of an intense critical review in the light of new scientific theories which try to combine the principles of both general relativity and quantum theory—called theories of quantum gravity. This book considers the way string theory shapes its own account of spacetime disappearance from the fundamental level.

Noncommutative Geometry and Physics 3

Proceedings of the Noncommutative Geometry and Physics 2008, on K-theory and D-brane, Shonan Village Center, ... the relationship between boundary conformal field theory and K-theory, and consists in regarding open string boundary ...

Author: Giuseppe Dito

Publisher: World Scientific

ISBN: 9789814425018

Category: Mathematics

Page: 537

View: 790

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Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.

Noncommutative Structures in Mathematics and Physics

Non-commutative field theories in the setup discussed here appear also in string theory. In [41] it was shown that the physics ... It has been suggested that the effects of UV/IR mixing could be understood from a string perspective [7].

Author: S. Duplij

Publisher: Springer Science & Business Media

ISBN: 9789401008365

Category: Science

Page: 484

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A presentation of outstanding achievements and ideas, of both eastern and western scientists, both mathematicians and physicists. Their presentations of recent work on quantum field theory, supergravity, M-theory, black holes and quantum gravity, together with research into noncommutative geometry, Hopf algebras, representation theory, categories and quantum groups, take the reader to the forefront of the latest developments. Other topics covered include supergravity and branes, supersymmetric quantum mechanics and superparticles, (super) black holes, superalgebra representations, and SUSY GUT phenomenology. Essential reading for workers in the modern methods of theoretical and mathematical physics.

Noncommutative Geometry and Physics 3

The classic example of this is in conjunction with topological string theory and Kontsevich's homological mirror ... From the mathematical perspective of noncommutative geometry alone, the formalism thus enables us to develop more tools ...

Author: Giuseppe Dito

Publisher: World Scientific

ISBN: 9789814425025

Category: Mathematics

Page: 536

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Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field. It is an important topic both for mathematics and physics. Contents:K-Theory and D-Branes, Shonan:The Local Index Formula in Noncommutative Geometry Revisited (Alan L Carey, John Phillips, Adam Rennie and Fedor A Sukochev)Semi-Finite Noncommutative Geometry and Some Applications (Alan L Carey, John Phillips and Adam Rennie)Generalized Geometries in String Compactification Scenarios (Tetsuji Kimura)What Happen to Gauge Theories under Noncommutative Deformation? (Akifumi Sako)D-Branes and Bivariant K-Theory (Richard J Szabo)Two-Sided Bar Constructions for Partial Monoids and Applications to K-Homology Theory (Dai Tamaki)Twisting Segal's K-Homology Theory (Dai Tamaki)Spectrum of Non-Commutative Harmonic Oscillators and Residual Modular Forms (Kazufumi Kimoto and Masato Wakayama)Coarse Embeddings and Higher Index Problems for Expanders (Qin Wang)Deformation Quantization and Noncommutative Geometry, RIMS:Enriched Fell Bundles and Spaceoids (Paolo Bertozzini, Roberto Conti and Wicharn Lewkeeratiyutkul)Weyl Character Formula in KK-Theory (Jonathan Block and Nigel Higson)Recent Advances in the Study of the Equivariant Brauer Group (Peter Bouwknegt, Alan Carey and Rishni Ratnam)Entire Cyclic Cohomology of Noncommutative Manifolds (Katsutoshi Kawashima)Geometry of Quantum Projective Spaces (Francesco D'Andrea and Giovanni Landi)On Yang–Mills Theory for Quantum Heisenberg Manifolds (Hyun Ho Lee)Dilatational Equivalence Classes and Novikov–Shubin Type Capacities of Groups, and Random Walks (Shin-ichi Oguni)Deformation Quantization of Gauge Theory in ℝ4 and U(1) Instanton Problems (Yoshiaki Maeda and Akifumi Sako)Dualities in Field Theories and the Role of K-Theory (Jonathan Rosenberg)Dualities in Field Theories and the Role of K-Theory (Jonathan Rosenberg) Readership: Researchers and graduate students in Mathematical Physics and Applied Mathematics. Keywords:Noncommutative Geometry;Deformation Quantizations;D-Brane;K-Theory;T-Duality

Noncommutative Geometry and Number Theory

[G] K. Gawedzki, Lectures on conformal field theory, in 'Quantum Fields and Strings: a Course for Mathematicians', P. Deligne et al. editors, American Mathematical Society 1999; pp 727-805. [GSW] M. Green, J.H. Schwarz, E. Witten, ...

Author: Caterina Consani

Publisher: Springer Science & Business Media

ISBN: 9783834803528

Category: Mathematics

Page: 372

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In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.

Quantum Field Theory Perspective and Prospective

It is clear that one can describe this as a replacement of commutative by noncommutative geometry. However, despite some effort, no deep connections have been found as yet between Matrix Theory and the extensive mathematical literature ...

Author: Cécile Dewitt-Morette

Publisher: Springer Science & Business Media

ISBN: 9789401145428

Category: Science

Page: 403

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It has been said that `String theorists talk to string theorists and everyone else wonders what they are saying'. This book will be a great help to those researchers who are challenged by modern quantum field theory. Quantum field theory experienced a renaissance in the late 1960s. Here, participants in the Les Houches sessions of 1970/75, now key players in quantum field theory and its many impacts, assess developments in their field of interest and provide guidance to young researchers challenged by these developments, but overwhelmed by their complexities. The book is not a textbook on string theory, rather it is a complement to Polchinski's book on string theory. It is a survey of current problems which have their origin in quantum field theory.

FROM ELECTRONS TO ELEPHANTS AND ELECTIONS

Among them, the most attractive and promising ones seem to be string theory, non-commutative geometry and loop ... from the perspective of topological quantum field theory and superstring theory or from that of non-commutative geometry.

Author: Shyam Wuppuluri

Publisher: Springer Nature

ISBN: 9783030921927

Category: Biomathematics

Page: 886

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This highly interdisciplinary book, covering more than six fields, from philosophy and sciences all the way up to the humanities and with contributions from eminent authors, addresses the interplay between content and context, reductionism and holism and their meeting point: the notion of emergence. Much of todays science is reductionist (bottom-up); in other words, behaviour on one level is explained by reducing it to components on a lower level. Chemistry is reduced to atoms, ecosystems are explained in terms of DNA and proteins, etc. This approach fails quickly since we cant cannot extrapolate to the properties of atoms solely from Schrodinger's equation, nor figure out protein folding from an amino acid sequence or obtain the phenotype of an organism from its genotype. An alternative approach to this is holism (top-down). Consider an ecosystem or an organism as a whole: seek patterns on the same scale. Model a galaxy not as 400 billion-point masses (stars) but as an object in its own right with its own properties (spiral, elliptic). Or a hurricane as a structured form of moist air and water vapour. Reductionism is largely about content, whereas holistic models are more attuned to context. Reductionism (content) and holism (context) are not opposing philosophies in fact, they work best in tandem. Join us on a journey to understand the multifaceted dialectic concerning this duo and how they shape the foundations of sciences and humanities, our thoughts and, the very nature of reality itself.

Are We There Yet The Search for a Theory of Everything

In one way, this kind of unification is similar to Kaluza-Klein compactification in string theory. ... Why should one prefer noncommutative geometry over the usual field theory approach when it contains almost as many parameters and ...

Author: Moataz H. Emam

Publisher: Bentham Science Publishers

ISBN: 9781608052141

Category: Science

Page: 130

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We live in exciting times. the frontiers of physics have been pushed to unprecedented horizons. the Holy Grail of fundamental physics research today is to find and describe a theory that explains, at least in principle, all physical phenomena, which in turns explains chemistry, biology and other material sciences. This, however, is not without controversy. the current candidate for such a theory is known as string or superstring theory. It suffers from the problem of being a purely mathematical science with no experimental backing and belief in it has been criticized as bordering on "faith" as opposed to scientific scrutiny. On the other hand the recent switching-on of our most advanced experimental tool, the Large Hadron Collider in Switzerland, gives new hope in our search for clues as to what the universe is made of on a fundamental level. What happened exactly on, or even before, the Big Bang? Where are we coming from and where are we going? Questions that have never been addressed before by physicists. the game is afoot and the search is on. This book contains articles by leading physicists describing the current situation. Among them are proponents as well as opponents of string theory, proponents of other ideas, and experimentalists.