More on #QuantumFieldTheory anomalies in #topological #insulators😎 Learn about the non-perturbative global anomalies in 3D and discuss their connection to topological states in 4D at https://enabla.com/pub/1105/about; the video lecture is supplemented by carefully-crafted lecture notes🔥

The anomalies we studied so far manifested themselves as non-conserved currents, corresponding to gauge non-invariance of the partition function in the presence of background fields. We showed that the anomalies in 2D signal the existence of topological states in 3D, the connection being the symmetry restoration due to the flow of a conserved quantity from bulk to edge. It is natural to ask if there is a similar connection between a topological state in 4D and an anomaly in 3D, but this does not seem likely, since the anomalies we discussed so far are present only in even D. It turns out, however, that there is a different class of anomalies that do appear in odd dimensions. In this class, we discuss global anomalies, which are associated with a change of the partition function over global gauge transformations. We first discuss how a Chern-Simons action can be non-invariant under a global gauge transformation if it has non-integer level. We then return to the edge theory of a topological insulator and understand whether the system is invariant or not under this transformation. Studying the index theorem in a system with a boundary, we understand that neither the bulk nor the edge is invariant in isolation, so we need both to have a consistent theory.

Our lectures are #free & #OpenAccess; the easiest way for you to support our project is to share this post, follow our account, and ask a few questions on Enabla. Thank you!🙏

Remember the half-quantized #quantum #HallEffect paradox we introduced a week ago? Today we explain this effect and discuss why it is present in #topological #insulators but not in #superconductors🤓

Explore the #QFT videos & lecture notes and ask your questions at https://enabla.com/pub/1103/about

All our lectures are #free and #OpenAccess; the easiest way for you to support our project is to share this post, follow our account, and ask a few questions on Enabla. Thank you!🙏

🤔What can go wrong when you have two #Postdocs named Daniel, both Irish 🇮🇪 ? I don't know, but what can go well is to calculate with #DFT what happens when you apply an #electric field on #insulators. More details in our paper (👉🏻https://journals.aps.org/prb/abstract/10.1103/PhysRevB.106.174105) with colleagues from the #UniversityOfLiege in #Belgium 🇧🇪. #UniversiteParisSaclay #centralesupelec 🇫🇷

I have been collecting glass insulators for over 20 years. These were actually used around the world on telegraph, telephone, and electric power lines. The oldest I have is from the 1860s. They come in just about every color.

If you want to know more, feel free to ask, but also check out these websites¹².
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¹https://www.insulators.info
²https://www.nia.org

#hobbies #antiques #glass #electric #insulators

I also bought a T-shirt from the #Insulators Union because I love their #salamander logo.

#pylons #insulators

You only need half the number of insulators on the left, and they can have much lower tensile strength: way cheaper.

So presumably the ones on the right are only used so the wind doesn't blow the big wires sideways.

So why aren't they always like the right?