Anomaly Detection in Geostationary Satellites

Abstract

As Eugene Wigner showed in 1939 for the Poincaré algebra, fundamental particles can be classified using symmetry algebras. In a universe including gravity, the Poincaré algebra cannot be the correct symmetry algebra, as this is the symmetry algebra for flat space. Instead, one should consider a symmetry algebra of asymptotic symmetries, which preserve only the asymptotic structure of gravity. Many of these asymptotic symmetries are not physically useful and are therefore considered “trivial.”

In this thesis, we give a new quantum definition of trivial symmetries, namely that a symmetry is trivial if it does not change which fundamental particles are found in a classification. We then specialize to three-dimensional asymptotically Anti-de-Sitter space. To calculate which symmetries are trivial, we first determine the second cohomology group of the asymptotic symmetries. Using the second cohomology group, it is then found that the useful asymptotic symmetry algebra is given by w⊕w⊕Rw \oplus w \oplus \mathbb{R}w⊕w⊕R, where www is the Witt algebra (centerless Virasoro) algebra, whereas the standard definition of trivial symmetry gives w⊕ww \oplus ww⊕w as the useful symmetry algebra. The extra factor of R\mathbb{R}R is interpreted as a kind of center-of-mass momentum.