The novel method of scaling algebras allows one to compute and classify the short distance (scaling) limit of any local relativistic $C^*$-dynamical system and to determine its symmetry structure. The approach is based on an adaptation of ideas from renormalization group theory to the $C^*$-algebraic setting [cf. D. Buchholz and R. Verch, Rev. Math. Phys. 7, No. 8, 1195-1239 (1995; Zbl 0842.46052); D. Buchholz, Ann. Inst. Henri Poincaré, Phys. Théor. 64, No. 4, 433-459 (1996; Zbl 0857.46055)].

46L60, 81T05, 46N50, 81T17

local relativistic $C^*$-dynamical systems, scaling algebras, symmetry structure, renormalization group theory