Spacetime and observer space symmetries in the language of Cartan geometry

Understand

We introduce a definition of symmetry generating vector fields on manifolds which are equipped with a first-order reductive Cartan geometry.

• We apply this definition to a number of physically motivated examples and show that our newly introduced notion of symmetry agrees with the usual notions of symmetry of affine, Riemann-Cartan, Riemannian and Weizenb\"ock geometries, which are conventionally used as spacetime models.
• Further, we discuss the case of Cartan geometries which can be used to model observer space instead of spacetime.
• We show which vector fields on an observer space can be interpreted as symmetry generators of an underlying spacetime manifold, and may hence be called "spatio-temporal".