Skip to main content Accessibility help
×
Home
Hostname: page-component-6c8bd87754-sbrr8 Total loading time: 0.315 Render date: 2022-01-16T19:25:22.008Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": true, "newCiteModal": false, "newCitedByModal": true, "newEcommerce": true, "newUsageEvents": true }

24 - Algebraic approach to Quantum Gravity II: noncommutative spacetime

from Part V - Effective models and Quantum Gravity phenomenology

Published online by Cambridge University Press:  26 October 2009

Daniele Oriti
Affiliation:
Universiteit Utrecht, The Netherlands
Get access

Summary

Introduction

In this chapter we present noncommutative geometry (NCG) not as a ‘theory of everything’ but as a bridge between any future, perhaps combinatorial, theory of Quantum Gravity and the classical continuum geometry that has to be obtained in some limit. We consider for the present that NCG is simply a more general notion of geometry that by its noncommutative nature should be the correct setting for the phenomenology and testing of first next-to-classical Quantum Gravity corrections. Beyond that, the mathematical constraints of NCG may give us constraints on the structure of Quantum Gravity itself in so far as this has to emerge in a natural way from the true theory.

Also in this chapter we focus on the role of quantum groups or Hopf algebras as the most accessible tool of NCG, along the lines first introduced for Planck scale physics by the author in the 1980s. We provide a full introduction to our theory of ‘bicrossproduct quantum groups’, which is one of the two main classes of quantum group to come out of physics (the other class, the q-deformation quantum groups, came out of integrable systems rather than Quantum Gravity). The full machinery of noncommutative differential geometry such as gauge theory, bundles, quantum Riemannian manifolds, and spinors (at least in principle) has also been developed over the past two decades; these topics are deferred to a third article.

Type
Chapter
Information
Approaches to Quantum Gravity
Toward a New Understanding of Space, Time and Matter
, pp. 466 - 492
Publisher: Cambridge University Press
Print publication year: 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)
5
Cited by

Send book to Kindle

To send this book to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Send book to Dropbox

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Dropbox.

Available formats
×

Send book to Google Drive

To send content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about sending content to Google Drive.

Available formats
×