2015/08/04 by Blagoje Oblak, Oblak, Blagoje · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Group Theory (math.GR) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Mathematics and Applications #Physics Education (physics.ed-ph) #Relativity and Gravitational Theory
paper · pdf · doi:10.48550/arxiv.1508.00920
openalex publication_date 2015/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In these lecture notes we review the isomorphism between the (connected) Lorentz group and the set of conformal transformations of the sphere. More precisely, after establishing the main properties of the Lorentz group, we show that it is isomorphic to the group SL(2,C) of complex 2 by 2 matrices with unit determinant. We then classify conformal transformations of the sphere, define the notion of null infinity in Minkowski space-time, and show that the action of Lorentz transformations on the celestial spheres at null infinity is precisely that of conformal transformations. In particular, we discuss the optical phenomena observed by the pilots of the "Millenium Falcon" during the jump to lightspeed.