Noncommutative spacetimes. Symmetries in noncommutative geometry and field theory
type: Item
instance of: scholarly article
title: Noncommutative spacetimes. Symmetries in noncommutative geometry and field theory
zbMATH Open document ID: 1177.81004
DOI: 10.1007/978-3-540-89793-4
author: Paolo Aschieri
author: Fedele Lizzi
author: Julius Wess
author: Marija Dimitrijević
author: Peter P. Kulish
published in: Lecture Notes in Physics
publication date: 2008-12-09T00:00:00Z
review text: In the first nine chapters, this book records approach to non-commutative differential geometry and its applications to physics developed over the past few years by the group led by Julius Wess. The final chapter summarises main themes of non-commutative geometry pursued by Julius Wess from 1989 until his death in 2007. The main theme of the book is physics and symmetries of spaces deformed by the twist or the \(*\)-product deformations (Moyal deformation of algebras of functions). The book is split into two parts. The first part is devoted to physical aspects of deformed field theory (chapters 1--5), the second part is devoted to foundations and applications of non-commutative geometries (chapters 6--9). The first three chapters, authored by Julius Wess, initially describe the \(*\)-product, differential calculus, differential operators and gauge transformations on deformed spaces. Subsequently gauge theory and the Einstein gravity are developed on deformed spaces. Chapters 4 and 5 are authored by Marija Dimitrijević and compare twisted gauge theory developed in Chapters 1--3 with the Seiberg-Witten approach to non-commutative field theory, and also describe gauge theory on the \(\kappa\)-deformed space. The second part starts with Chapter 6, written by Fedele Lizzi. This chapter is devoted to foundations of non-commutative geometry, and first describes the algebras of functions on classical spaces and then their deformation in terms of the Moyal \(*\)-product. Chapters 7 and 8 are written by Paolo Aschieri and start with an introduction to quantum groups (with particular attention paid to the deformations of Hopf algebras by twists) and culminate with the description of the twisted Poincaré algebra and the \(*\)-deformation of Einstein's gravity. Chapter 9, authored by Petr Kulish, provides one with a brief introduction to the Quantum Inverse Scattering Method (of solving integrable systems in quantum mechanics, in particular spin chains), and then analyses twists…
reviewed by: Tomasz Brzeziński
Mathematics Subject Classification ID: 81-02
Mathematics Subject Classification ID: 81T75
Mathematics Subject Classification ID: 58B34
Mathematics Subject Classification ID: 81T70
Mathematics Subject Classification ID: 81T13
Mathematics Subject Classification ID: 81V17
Mathematics Subject Classification ID: 81R50
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 53D55
Mathematics Subject Classification ID: 81R25
Mathematics Subject Classification ID: 81U40
Mathematics Subject Classification ID: 81R12
Mathematics Subject Classification ID: 82B20
Mathematics Subject Classification ID: 83C45
zbMATH DE Number: 5379961
zbMATH Keywords: noncommutative space
zbMATH Keywords: *-deformation
zbMATH Keywords: twisting
zbMATH Keywords: gauge theory
zbMATH Keywords: gravity
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-3-540-89793-4
OpenAlex ID: W4244293910
description: scientific article; zbMATH DE number 5379961