tag:blogger.com,1999:blog-2381900080106522441.post5311759548711045586..comments2022-11-12T13:01:02.179+01:00Comments on relatively quantum: Yang-Mills analogues of the ambiguities in defining LQG geometric operatorsNorberthttp://www.blogger.com/profile/04965554394207041308noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2381900080106522441.post-92039497580191988292017-10-25T17:37:55.666+02:002017-10-25T17:37:55.666+02:00hmmmmmhmmmmmJeCksOnhttps://www.blogger.com/profile/12087778649552689484noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-49405531893849562162016-03-25T12:40:54.648+01:002016-03-25T12:40:54.648+01:00David, thanks for your comment.
We can divide th...David, thanks for your comment. <br /><br />We can divide the ambiguities discussed here in two classes: the first class is coming from the choice of observables. This choice is however related to a physical choice about how you prepare your experiment. Different observable constructions refer to different ways of defining which area you mean, i.e. with respect to what other structure you locate this area. In general, it is hard, if not impossible, to unambiguously translate questions between such preferred elementary sets of observables. For predictions, I would then trust always those observables where we have an unambiguous quantum analog of the classical function. <br /><br />This leaves the freedom of rescaling the metric by a constant parameter $\beta$. Concerning this, there has been some development in the literature recently pointing towards the self-dual value $\beta = i$ being preferred, see the links below. As a little background: the original Ashtekar variables in which the classical theory simplifies the most are obtained by the choice $\beta = i$. However, people were not successful in constructing a Hilbert space for this choice of variables (we are lacking an inner product implementing the rather complicated reality conditions). On the other hand, the Hilbert space can be rigorously constructed for real $\beta$. The attitude that I would now take is to check whether a certain value of $\beta$ is preferred in the quantum theory. As discussed in the references, there are several hints now for $\beta = i$, obtained from analytically continuing results for real $\beta$. If this turns out to be way to go, then this would solve the problem of this ambiguity. <br /><br />More answers to the other criticism you cited are scattered in the literature. I am planning to come back to them at some point in the future. <br /><br />http://arxiv.org/abs/1212.4060<br />http://arxiv.org/abs/1303.4752<br />http://arxiv.org/abs/1305.6714<br />http://arxiv.org/abs/1402.4138Norberthttps://www.blogger.com/profile/04965554394207041308noreply@blogger.comtag:blogger.com,1999:blog-2381900080106522441.post-44454731436342217002016-03-24T09:55:06.944+01:002016-03-24T09:55:06.944+01:00"... the reason for the ambiguity in the geom..."... the reason for the ambiguity in the geometric operators in loop quantum gravity is the freedom in choosing a metric on which the connection variables are based." From the point of view of making predictions, I would say that such freedom is a flaw in loop quantum gravity.<br />It might be helpful for someone to give a critique of Motl's critique of loop quantum gravity.<br /><a href="http://motls.blogspot.com/2004/10/objections-to-loop-quantum-gravity.html" rel="nofollow">objections-to-loop-quantum-gravity.html, Motl's blog, 2004</a>David Brownhttps://www.blogger.com/profile/10537922851243581921noreply@blogger.com