Heuristics for Lorentz violations in LQG

Slight energy dependences in the speed of light can accumulate over time,
allowing for possible detection or exclusion of such effects. Highly energetic
photons emitted e.g. by a supernova are in particularly useful for such studies.

Predictions for possible Lorentz violations are a key area of interesting phenomenology in quantum gravity. Within loop quantum gravity, it has not been possible so far to reliably extract predictions for Lorentz violations. Existing claims were based on simplified toy models inspired by LQG, but not implied. This situation hasn’t changed so far, but there is an interesting development which hints at which order we might expect such Lorentz violations to be found.

Elements of loop quantum gravity

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.