geometric algebraic and topological methods for quantum field theory proceedings of the 2013 villa de leyva summer school

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Geometric Algebraic And Topological Methods For Quantum Field Theory

Author : Leonardo Cano
ISBN : 9789814730891
Genre : Mathematics
File Size : 39. 71 MB
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Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics. It is aimed at graduate students and researchers in physics or mathematics, and offers an introduction to the topics discussed in the two weeks of the summer school: operator algebras, conformal field theory, black holes, relativistic fluids, Lie groupoids and Lie algebroids, renormalization methods, spectral geometry and index theory for pseudo-differential operators.

Geometric Algebraic And Topological Methods For Quantum Field Theory

Author : Sylvie Payche
ISBN : 9789814460057
Genre : Science
File Size : 52. 78 MB
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Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory. This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.

Geometric And Topological Methods For Quantum Field Theory

Author : Alexander Cardona
ISBN : 9781107026834
Genre : Science
File Size : 42. 59 MB
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"Based on lectures given at the renowed Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics"--

Quantization Geometry And Noncommutative Structures In Mathematics And Physics

Author : Alexander Cardona
ISBN : 9783319654270
Genre : Science
File Size : 89. 88 MB
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This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.

Facettenreiche Mathematik

Author : Katrin Wendland
ISBN : 9783834881731
Genre : Mathematics
File Size : 31. 34 MB
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Dieser Band versammelt zweiundzwanzig spannende Beiträge, in denen verschiedene Mathematikerinnen ihre Forschungsgebiete vorstellen. Dabei werden nur Schulkenntnisse in Mathematik vorausgesetzt, und der Bogen wird von klassischen Resultaten bis zur aktuellen Forschung gespannt. Das Buch vermittelt eindrucksvoll den Facettenreichtum der modernen Mathematik und lädt dazu ein, sich von der Faszination der Mathematikerinnen für ihre Forschungsgebiete anstecken zu lassen.

Der Vierfarbensatz

Author : Rudolf Fritsch
ISBN : 3411151412
Genre : Four-color problem
File Size : 69. 91 MB
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Analysis Und Mathematische Physik

Author : Hans Triebel
ISBN : 3446133925
Genre : Differential equations
File Size : 27. 61 MB
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Ein Aufleuchtender Blitz

Author : Arild Stubhaug
ISBN : 3540418792
Genre : Mathematics
File Size : 22. 15 MB
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Auszüge aus einer Rezension der englischen Ausgabe: "Ein mathematisches Genie, das viel zu früh starb und das quasi erst auf dem Totenbett die Stelle angeboten bekam, die seinem Leben eine finanzielle Basis gegeben und ihm eine große Karriere eröffnet hätte... In der Mathematikgeschichte ist eine Biographie, aus der man leicht ein Film-Drehbuch machen könnte, kein Einzelfall (Galois, Ramanujan, ...), im vorliegenden Buch wird das Leben von Abel liebevoll und sehr ausführlich nachgezeichnet. Man kann das Buch als erste Einführung in die von Abel entwickelte Mathematik lesen. (Es gibt in dem Buch aber keine einzige Formel, wirklich schwierig wird es an keiner Stelle.) Es bietet auch die Möglichkeit, viel Interessantes aus der europäischen, insbesondere der norwegischen Geschichte zu Beginn des neunzehnten Jahrhunderts zu erfahren. ..." Internet Portal der DMV, http://www.mathematik.de

De Nobilitate Et Praecellentia Foeminei Sexus

Author : Heinrich Cornelius Agrippa von Nettesheim
ISBN : 3826012623
Genre : Feminism
File Size : 63. 39 MB
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Sterne Und Sternhaufen

Author : Cecilia Helena Payne Gaposchkin
ISBN : 9783322862662
Genre : Science
File Size : 29. 68 MB
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