Particles in LQG: Are There Alternatives to Braids?

[twistor]

Though a major collection of LQG researchers believe that particles raise in LQG by braiding (see http://arxiv.org/abs/1109.0080 and http://arxiv.org/abs/0903.1376), are there alternatives any to braids?

 

[marcus]

Though a major collection of LQG researchers believe that particles raise in LQG by braiding (see http://arxiv.org/abs/1109.0080 and http://arxiv.org/abs/0903.1376), are there alternatives any to braids?

Heh heh, twistor in the 2011 paper's authors you do not have a MAJOR collection of people currently doing LQG research. If you go back before 2011 you would find quite a few! E.g. Lee Smolin, Fotini Markopoulou.
But there has been no interest in braid matter that I know of in the past 3 years.
Your 2011 paper has been cited twice since it came out, in each case by an author without institutional affiliation and no significant LQG track record.

My thought is that you do not need to worry about braids, you need a 2014 view of how matter might be included in Spin Foam or LQG. Here's a 2014 view, in the conclusions of Wieland's thesis:

At the end of Wieland's thesis there is a section (pages 136, 137) on future research interests.
It's worth seeing how they are laid out. One very interesting section (which I'll skip) is on the "flatness problem." Another section is on INCLUSION OF MATTER which is interesting enough that I want to quote in full:

== http://tel.archives-ouvertes.fr/docs/00/95/24/98/PDF/diss.pdf pages 136-137==
Inclusion of matter
To aim at a phenomenology of loop quantum gravity [201–203], strong enough to turn it falsifiable, we need to better understand how matter (our “rulers” and “clocks”) couples to the theory. Unfortunately, after decades of research, we still cannot say much about this issue. To overcome this trouble, I can see four roads to attack the problem, three of which I would like to study by myself:

(i) At first, there is what has been always tried in loop quantum gravity when it comes to this problem. Take any standard matter described by some Lagrangian, put in on an irregular lattice corresponding to a spin network state and canonically quantise. Although this approach was tried for all kinds of matter it led to very little physical insight. I think it is time to try different strategies.

(ii) The first idea that comes to my mind originates from an old paper by t’ Hooft [204]. I think it is a logical possibility that loop quantum gravity already contains a certain form of matter. If we look at the curvature of our models we find it is concentrated on the two-dimensional surfaces of the spinfoam faces. This curvature has a non-vanishing Ricci part which we can use (employing Einstein’s equations) to assign an energy momentum tensor to the spinfoam face. Following this logic one may then be able to reformulate the dynamics of spinfoam gravity as a scattering process of these two-dimensional worldsheets (that now carry energy-momentum) in a locally flat ambient space.

(iii) Loop quantum gravity is a theory of quantised area-angle-variables. I think this suggests not to start from the standard model that couples matter to tetrad (i.e. length-angle) variables. Instead we should take the fundamental discreteness of loop quantum gravity seriously, and try to add matter fields to the natural geometrical structures appearing, e.g. the two-dimensional spinfoam faces. In fact, when looking at the kinetic term of the action (3.46) a candidate immediately appears. We could just replace the commuting (π, ω) spinors by anti-commuting Weyl (Majorana) spinors, yielding a simple coupling of uncharged spin 1/2 particles to a spinfoam.

(iv) The recent understanding of loop quantum gravity in terms of twistors is mirrored [205–209] by similar developments in the study of scattering amplitudes of e.g. N = 4 super Yang–Mills theory . It is tempting to say these results all point towards the same direction eventually yielding a twistorial framework for all interactions.
==endquote==

 

[marcus]

Though a major collection of LQG researchers believe that particles raise in LQG by braiding (see http://arxiv.org/abs/1109.0080 and http://arxiv.org/abs/0903.1376), are there alternatives any to braids?

As I indicated, this post is a bit out of touch because for some years now LQG researchers have shown little or no interest in BRAID matter. What has recently been the most often cited pedagogical review (Rovelli's 2011 Zakopane lectures) discusses inclusion of matter by coloring spin network links and nodes. I don't recall any mention of braiding.

However it's worth highlighting another idea that has come up. I'll quote a portion of the previous post:

At the end of Wieland's thesis there is a section (pages 136, 137) on future research interests…

== http://tel.archives-ouvertes.fr/docs/00/95/24/98/PDF/diss.pdf pages 136-137==
Inclusion of matter
To aim at a phenomenology of loop quantum gravity [201–203], …
...
(iv) The recent understanding of loop quantum gravity in terms of twistors is mirrored [205–209] by similar developments in the study of scattering amplitudes of e.g. N = 4 super Yang–Mills theory . It is tempting to say these results all point towards the same direction eventually yielding a twistorial framework for all interactions.
==endquote==
Here, to be a bit more specific in case they mean something to you, are some of the references cited:

[206] T. Adamo, M. Bullimore, L. Mason, and D. Skinner, “Scattering amplitudes and Wilson loops in twistor space,” J. Phys. A: Math. Theor. 44 (2011) 454008, arXiv:1104.2890.
[207] J. J. Heckman and H. Verlinde, “Instantons, Twistors, and Emergent Gravity,” arXiv:1112.5210.
[208] J. J. Heckman and H. Verlinde, “Gravity Amplitudes from a Gaussian Matrix Model,” arXiv:1112.5209.
[209] F. Cachazo, L. Mason, and D. Skinner, “Gravity in Twistor Space and its Grassmannian Formulation.” 2012

 

[ftr]

Though a major collection of LQG researchers believe that particles raise in LQG by braiding (see http://arxiv.org/abs/1109.0080 and http://arxiv.org/abs/0903.1376), are there alternatives any to braids?

See this old thread


https://www.physicsforums.com/showthread.php?t=445727&page=2

 

[marcus]

See this old threadhttps://www.physicsforums.com/showthread.php?t=445727

Yes! That old thread from back in 2010 still has some good stuff! For instance, Wen Zhao talking about LQG testing in relation to B-mode observation of CMB, and mentioning BICEP. He looked forward (already back in 2010) to the swirls in ancient light that we heard about in March of 2014.

And it was noticeable already in 2010 that interest in "braid matter" was fading, so people were realizing that that had to work out other ways of building matter into LQG.

So I like Wieland's sketch of 4 possible ways of doing that--three of which he personally finds interesting. I quoted his list back in post #2 of this thread.