Quantum seminar | 28 August 2024

In this educational seminar, we consider the intriguing relationship between two seemingly unrelated concepts: vector spherical harmonics and the proper orthochronous Lorentz group.

On the one hand, vector spherical harmonics are a powerful tool widely used in the study of optical systems. On the other hand, the proper orthochronous Lorentz group is a subgroup of the Lorentz group, consisting of rotations and boosts.

Our exploration will reveal a connection between vector spherical dipoles, which are specific types of vector spherical harmonics, and the movements of stars on the celestial sphere under Lorentz transformations.

Main paper/arXiv, related to the seminar, and other references:

1. Oblak, Blagoje. From the Lorentz Group to the Celestial Sphere. arXiv, 4 Aug. 2015, doi:10.48550/arXiv.1508.00920.
2. González-Miret Zaragoza, Luis. Möbius Transformations. Dissertation, 2019, idus.us.es/handle/11441/127035.
3. Needham, Tristan. Visual Complex Analysis. Clarendon Press, 1997.
4. Zee, Anthony. Group Theory in a Nutshell for Physicists. Princeton UP, 2016.