  The standard concept of scaling limits of distributions on manifolds is
reformulated, and then a new framework for scaling at boundary points is
provided. Next, we introduce a class of so-called L1 - KMS states, which is
subsequently fully characterized for the Rindler wedge. Using these tools, we
compute rigorously the scaling limit of the regular KMS state of the free
scalar quantum field on the Rindler horizon. Thereby, we correct certain
inaccurate results of founding paper [1], nevertheless fully corroborating the
physical essence of them.
