Geometry And Quantum Field Theory
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Quantum Mechanics Quantum Field Theory
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Author : R. Mirman
language : en
Publisher: iUniverse
Release Date : 2004-12
Quantum Mechanics Quantum Field Theory written by R. Mirman and has been published by iUniverse this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12 with Science categories.
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Geometry And Quantum Field Theory
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Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Geometry And Quantum Field Theory 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 1995 with Science categories.
The first title in a new series, this book explores topics from classical and quantum mechanics and field theory. The material is presented at a level between that of a textbook and research papers making it ideal for graduate students. The book provides an entree into a field that promises to remain exciting and important for years to come.
Geometry And Quantum Field Theory
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Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Geometry And Quantum Field Theory 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 1995 with Mathematics categories.
Exploring topics from classical and quantum mechnanics and field theory, this book is based on lectures presented in the Graduate Summer School at the Regional Geometry Institute in Park City, Utah, in 1991. The chapter by Bryant treats Lie groups and symplectic geometry, examining not only the connection with mechanics but also the application to differential equations and the recent work of the Gromov school. Rabin's discussion of quantum mechanics and field theory is specifically aimed at mathematicians. Alvarez describes the application of supersymmetry to prove the Atiyah-Singer index theorem, touching on ideas that also underlie more complicated applications of supersymmetry. Quinn's account of the topological quantum field theory captures the formal aspects of the path integral and shows how these ideas can influence branches of mathematics which at first glance may not seem connected. Presenting material at a level between that of textbooks and research papers, much of the book would provide excellent material for graduate courses. The book provides an entree into a field that promises to remain exciting and important for years to come.
Geometric Methods For Quantum Field Theory
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Author : Hernan Ocampo
language : en
Publisher: World Scientific
Release Date : 2001-04-30
Geometric Methods For Quantum Field Theory written by Hernan Ocampo and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-04-30 with Science categories.
Both mathematics and mathematical physics have many active areas of research where the interplay between geometry and quantum field theory has proved extremely fruitful. Duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some striking recent examples of modern topics which stand on the borderline between geometry and analysis on the one hand and quantum field theory on the other, where the physicist's and the mathematician's perspective complement each other, leading to new mathematical and physical concepts and results.This volume introduces the reader to some basic mathematical and physical tools and methods required to follow the recent developments in some active areas of mathematical physics, including duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups. It comprises seven self-contained lectures, which should progressively give the reader a precise idea of some of the techniques used in these areas, as well as a few short communications presented by young participants at the school.
Operators Geometry And Quanta
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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.
Analysis Geometry And Quantum Field Theory
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Author : Clara L. Aldana
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Analysis Geometry And Quantum Field Theory written by Clara L. Aldana 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 2012 with Mathematics categories.
This volume contains the proceedings of the conference ``Analysis, Geometry and Quantum Field Theory'' held at Potsdam University in September 2011, which honored Steve Rosenberg's 60th birthday. The papers in this volume cover a wide range of areas, including Quantum Field Theory, Deformation Quantization, Gerbes, Loop Spaces, Index Theory, Determinants of Elliptic Operators, K-theory, Infinite Rank Bundles and Mathematical Biology.
Structural Aspects Of Quantum Field Theory In 2 Volumes
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Author : Gerhard Grensing
language : en
Publisher: World Scientific
Release Date : 2013-05-21
Structural Aspects Of Quantum Field Theory In 2 Volumes written by Gerhard Grensing and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-21 with Science categories.
'The book is primarily addressed to physicists. Nevertheless, as numerous examples are known in which exploration of the land where physics and mathematics overlap (and which quantum field theory definitely belongs to) resulted in important developments in mathematics, many mathematicians may also find this book interesting and even inspiring.'MathSciNetThis book is devoted to the subject of quantum field theory. It is divided into two volumes. The first can serve as a textbook on the main techniques and results of quantum field theory, while the second treats more recent developments, in particular the subject of quantum groups and noncommutative geometry, and their interrelation.The first volume is directed at graduate students who want to learn the basic facts about quantum field theory. It begins with a gentle introduction to classical field theory, including the standard model of particle physics, general relativity, and also supergravity. The transition to quantized fields is performed with path integral techniques, by means of which the one-loop renormalization of a self-interacting scalar quantum field, of quantum electrodynamics, and the asymptotic freedom of quantum chromodynamics is treated. In the last part of the first volume, the application of path integral methods to systems of quantum statistical mechanics is covered. The book ends with a rather detailed investigation of the fractional quantum Hall effect, and gives a stringent derivation of Laughlin's trial ground state wave function as an exact ground state.The second volume covers more advanced themes. In particular Connes' noncommutative geometry is dealt with in some considerable detail; the presentation attempts to acquaint the physics community with the substantial achievements that have been reached by means of this approach towards the understanding of the elusive Higgs particle. The book also covers the subject of quantum groups and its application to the fractional quantum Hall effect, as it is for this paradigmatic physical system that noncommutative geometry and quantum groups can be brought together.
Quantum Field Theory Supersymmetry And Enumerative Geometry
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Author : Daniel S. Freed
language : en
Publisher: American Mathematical Soc.
Release Date : 2006
Quantum Field Theory Supersymmetry And Enumerative Geometry 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 2006 with Mathematics categories.
This volume presents three weeks of lectures given at the Summer School on Quantum Field Theory, Supersymmetry, and Enumerative Geometry. With this volume, the Park City Mathematics Institute returns to the general topic of the first institute: the interplay between quantum field theory and mathematics.
Noncommutative Geometry Quantum Fields And Motives
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Author : Alain Connes
language : en
Publisher: American Mathematical Soc.
Release Date :
Noncommutative Geometry Quantum Fields And Motives written by Alain Connes 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 with Mathematics categories.
This book carries the unifying theme of the interaction among noncommutative geometry, theoretical physics and number theory. The detailed text, co-authored by Fields Medal winner Alain Connes, stresses the relevance of noncommutative geometry in dealing with two spaces: space-time and the space of prime numbers. The book includes significantly more detail than other monographs covering similar topics.
Geometric Approaches To Quantum Field Theory
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Author : Kieran Finn
language : en
Publisher: Springer Nature
Release Date : 2021-10-07
Geometric Approaches To Quantum Field Theory written by Kieran Finn and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-07 with Science categories.
The ancient Greeks believed that everything in the Universe should be describable in terms of geometry. This thesis takes several steps towards realising this goal by introducing geometric descriptions of systems such as quantum gravity, fermionic particles and the origins of the Universe itself. The author extends the applicability of previous work by Vilkovisky, DeWitt and others to include theories with spin 1⁄2 and spin 2 degrees of freedom. In addition, he introduces a geometric description of the potential term in a quantum field theory through a process known as the Eisenhart lift. Finally, the methods are applied to the theory of inflation, where they show how geometry can help answer a long-standing question about the initial conditions of the Universe. This publication is aimed at graduate and advanced undergraduate students and provides a pedagogical introduction to the exciting topic of field space covariance and the complete geometrization of quantum field theory.