2023/11/17 by Nakayama, Yu · 1 citation
#FOS: Physical sciences #High Energy Physics - Theory (hep-th)
paper · doi:10.48550/arxiv.2311.10254
We discuss the possibility of a central extension of the Poincaré algebra and the scaling Poincaré algebra. In more than two space-time dimensions, all the central extensions are trivial and can be removed. In two space-time dimensions, both the Poincaré algebra and the scaling Poincaré algebra have distinct non-trivial central extensions that cannot be removed. In higher dimensions, the central charges between dilatation and global U(1) symmetry may not be removed. Based on these central extensions, we give some examples of projective representations of the (scaling) Poincaré symmetry in two dimensions.