Author : Daniel S. Freed
Publisher : American Mathematical Soc.
Page : 476 pages
File Size : 35,30 MB
Release : 1995
Category : Science
ISBN : 9780821886830
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.
Author : Kieran Finn
Publisher : Springer Nature
Page : 212 pages
File Size : 15,11 MB
Release : 2021-10-07
Category : Science
ISBN : 3030852695
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.
Author : Ulrike Luise Tillmann
Publisher : Cambridge University Press
Page : 596 pages
File Size : 35,59 MB
Release : 2004-06-28
Category : Mathematics
ISBN : 9780521540490
The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.
Author : Hernan Ocampo
Publisher : World Scientific
Page : 530 pages
File Size : 40,36 MB
Release : 2001
Category : Science
ISBN : 9810243510
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.
Author : Jan Ambjørn
Publisher : Cambridge University Press
Page : 377 pages
File Size : 19,89 MB
Release : 1997-06-19
Category : Science
ISBN : 0521461677
Describes random geometry and applications to strings, quantum gravity, topological field theory and membrane physics.
Author : Ursula Carow-Watamura
Publisher : Springer Science & Business Media
Page : 316 pages
File Size : 47,27 MB
Release : 2005-02-21
Category : Mathematics
ISBN : 9783540239000
This volume reflects the growing collaboration between mathematicians and theoretical physicists to treat the foundations of quantum field theory using the mathematical tools of q-deformed algebras and noncommutative differential geometry. A particular challenge is posed by gravity, which probably necessitates extension of these methods to geometries with minimum length and therefore quantization of space. This volume builds on the lectures and talks that have been given at a recent meeting on "Quantum Field Theory and Noncommutative Geometry." A considerable effort has been invested in making the contributions accessible to a wider community of readers - so this volume will not only benefit researchers in the field but also postgraduate students and scientists from related areas wishing to become better acquainted with this field.
Author : Edoardo Ballico
Publisher : Springer
Page : 173 pages
File Size : 15,78 MB
Release : 2019-03-13
Category : Science
ISBN : 3030061221
This book collects independent contributions on current developments in quantum information theory, a very interdisciplinary field at the intersection of physics, computer science and mathematics. Making intense use of the most advanced concepts from each discipline, the authors give in each contribution pedagogical introductions to the main concepts underlying their present research and present a personal perspective on some of the most exciting open problems. Keeping this diverse audience in mind, special efforts have been made to ensure that the basic concepts underlying quantum information are covered in an understandable way for mathematical readers, who can find there new open challenges for their research. At the same time, the volume can also be of use to physicists wishing to learn advanced mathematical tools, especially of differential and algebraic geometric nature.
Author : Daniel S. Freed
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 49,2 MB
Release : 2006
Category : Mathematics
ISBN : 0821834312
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.
Author : Dmitri Fursaev
Publisher : Springer Science & Business Media
Page : 294 pages
File Size : 42,65 MB
Release : 2011-06-25
Category : Science
ISBN : 9400702051
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.
Author : Maurice A. de Gosson
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 38,42 MB
Release : 2006-08-06
Category : Mathematics
ISBN : 3764375752
This book offers a complete discussion of techniques and topics intervening in the mathematical treatment of quantum and semi-classical mechanics. It starts with a very readable introduction to symplectic geometry. Many topics are also of genuine interest for pure mathematicians working in geometry and topology.
