from Part III - Loop quantum gravity and spin foam models
Published online by Cambridge University Press: 26 October 2009
Introduction
The problem of background independent Quantum Gravity is the problem of defining a Quantum Field Theory of matter and gravity in the absence of an underlying background geometry (see Chapter 1 by Rovelli). Loop quantum gravity (LQG) is a promising proposal for addressing this difficult task. Its main predictions and underlying mathematical structure are described in Chapter 13 by Thiemann. Despite the steady progress of the field, dynamics remains to a large extend an open issue in LQG. Here we present the main ideas behind a series of proposals for addressing the issue of dynamics. We refer to these constructions as the spin foam representation of LQG. This set of ideas can be viewed as a systematic attempt at the construction of the path integral representation of LQG.
The spin foam representation is mathematically precise in 2 + 1 dimensions, so we will start this chapter by showing how it arises in the canonical quantization of this simple theory (more about 2+1 gravity can be found in Chapter 16 by Freidel). This toy model will be used to precisely describe the true geometric meaning of the histories that are summed over in the path integral of generally covariant theories.
In four dimensions similar structures appear. We call these constructions spin foam models as their definition is incomplete in the sense that at least one of the following issues remains unclear: (1) the connection to a canonical formulation, and (2) regularization independence (renormalizability).
To save this book to your Kindle, first ensure [email protected] 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 saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved 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.
To save 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 saving content to Dropbox.
To save 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 saving content to Google Drive.