  The canonical proper time formulation of relativistic dynamics provides a
framework from which one can describe the dynamics of classical and quantum
systems using the clock of those very systems. The framework utilizes a
canonical transformation on the time variable that is used to describe the
dynamics, and does not transform other dynamical variables such as momenta or
positions. This means that the time scales of the dynamics are described in
terms of the natural local time coordinates, which is the most meaningful
parameterization of phenomena such as the approach to equilibrium, or the back
reaction of interacting systems. We summarize the formalism of the canonical
proper time framework, and provide example calculations of the eigenvalues of
the hydrogen atom and near horizon description of a scalar field near a
Schwarzschild black hole.
