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Tuesday, July 19, 2016

Elements of loop quantum gravity

Elements of loop quantum gravity lecture outline


After some longer silence on this blog, I am happy to announce that the introductory lectures from which excerpts have appeared here before are finally online.

The lectures start with a general introduction to quantum gravity, including a theoretical motivation, possible experimental tests, and the previously posted list on approaches to the subject. There is also an improved (as compared to here) estimate on the local Lorentz invariance violation based on anomaly freedom of effective constraints. I am planning to write about it in more detail in the future.

Next, an introduction to loop quantum cosmology is given, a draft of which has appeared here before. The new version features some improvements in the presentation and some simplifications in the derivation.

The remaining part of the lectures introduces full loop quantum gravity with minimal technical details. The derivation of geometric operators is sketched and different approaches to the dynamics are discussed. Promising lines of current research are mentioned and evaluated. Exercises are included at the end of each section.

The present lecture notes are somewhat complementary to several other sets of lecture notes existing in the literature in that they refrain from technical details and give a broad overview of the subject, including motivations and current trends. If someone spots mistakes or has suggestions for a better presentation, I would be happy to hear about it.

Wednesday, June 8, 2016

Strings meet Loops via AdS/CFT (Helsinki Workshop on Quantum Gravity 2016)



This rerecorded talk was originally given at the Helsinki Workshop on Quantum Gravity on June 2, 2016. I was invited by the organisers to talk about a recent paper, which was intended as an invitation for people to become interested in the subject, as opposed to giving concrete and detailed results.

In particular, I am very much looking forward to discussions about this topic and criticism of the ideas, in particular from experts in string theory. In the long run, much can be gained in my point of view from intensifying the exchange between researchers in loop quantum gravity and string theory.

In this context, it is certainly worth pointing out a recent article by Sabine Hossenfelder for Quanta Magazine, as well as a blogpost of hers on the paper I wrote.

Wednesday, June 1, 2016

Graph superspositions and improved regularisations

Sum of graphs in loop quantum gravity
In loop quantum gravity, the elements of a certain basis in the Hilbert space
can be (roughly) interpreted as lattices. Generic quantum states can be constructed
as superpositions thereof and a priori have different properties which cannot
be realised at the level of individual lattices. 

Let us pick up the topic of extracting effective cosmological dynamics from loop quantum gravity again. Today’s post is about a recent paper by Emanuele Alesci and Francesco Cianfrani within their framework of “Quantum reduced loop gravity”. This version of loop quantum gravity is arrived at by a gauge fixing to the diagonal metric gauge at the quantum level (as opposed to the classical level as e.g. here), along with a truncation of the Hamiltonian constraint consistent with a spatially homogeneous setting (in particular, the non-trivial shift resulting from the gauge fixing is dropped). The simplified quantum dynamics resulting form this gauge fixing have allowed to compute the expectation value of the Hamiltonian constraint in suitable coherent states, leading to the effective Hamiltonian that one finds in loop quantum cosmology.

An open issue in this context has been to properly derive the so called “improved “ dynamics of loop quantum cosmology, which are consistent with observation and do not feature some unphysical properties of the original formulation. This is somewhat tricky if one uses standard connection variables along with a gauge group like SU(2) or U(1) for the following reason:

Wednesday, May 4, 2016

Progress on low spins

Transplanckian large spins decay into small spins under the dynamics
Fundamental (trans-Planckian) large spins are expected to decay into
many small spins under the dynamics. An explicit calculation showing
  this has been given now within group field theory. At the same time,
one can coarse grain the many small spins into few large spins to have
an effective continuum description. The precise relation between those
two, a priori distinct large spin regimes is so far unclear.  

The fundamentally important issue of low and high spins in the dynamics of LQG has been discussed in previous posts. In short, large geometries can be described using either many low or few large quantum numbers (SU(2) spins), but the respective dynamics needs to be interpreted with care. In particular, using large spins to describe continuum geometries requires to understand the renormalisation group flow of the theory. Most work in LQG has so far been in the context of large spins (without considering renormalisation), where calculations simplify drastically due to the availability certain asymptotic formulae for the SU(2) recouping coefficients with nice geometric interpretations. However, there seems to be some progress now on the low spin front. 

Monday, April 25, 2016

Is loop quantum gravity based on discretisations?

Sum of two spin networks for continuum limit of loop quantum gravity
Two spin networks, which can be interpreted as Hilbert space elements
describing truncations (or discretisations) of general relativity,
are summed. What is the physics of such states? 

This post is related to last week’s about criticism of loop quantum gravity and a comment I found in Sabine Hossenfelder’s blog. Saying that loop quantum gravity is based on discretisations quickly leads one to doubt that Lorentz invariance may be a property of LQG, as happened in the comment. So it seems worth to clear up this issue and precisely say in what context discretisations appear, in what context they don’t, and what this means for the physics that are described by LQG.

Thursday, April 21, 2016

Updates on some criticisms of loop quantum gravity

Criticism of loop quantum gravity: Lorentz violations, general relativity limit, ambiguities
Image from MySafetySign.com


In this post, we will gather some criticism which has been expressed towards loop quantum gravity and comment on the current status of the respective issues. The points raised here are the ones most serious in my own opinion, and different lists and assessments could be expressed by other researchers. 

Tuesday, April 12, 2016

Approaches to quantum gravity



Again as a part of a lecture series in preparation, I compiled a list of the currently largest existing research programmes aimed at finding a quantum theory of gravity (while unfortunately omitting some smaller, yet very interesting, approaches). A much more extensive account is given in here. For an historical overview, I recommend this paper.