# Classical Klein-Gordon theory is a free relativistic theory

The classical Klein-Gordon theory for a real scalar field is called a relativistic free theory.

It is called a free theory because the dynamics of the degrees of freedom in the momentum space of the Klein-Gordon theory are decoupled from each other. In other words, the Klein-Gordon theory is devoid of interactions among the excitations of the Klein-Gordon field in the momentum space.

Is the Klein-Gordon theory also devoid of interactions among the excitations of the Klein-Gordon field in the position space?

Why is the Klein-Gordon theory called a relativistic theory? Is it because the Klein-Gordon Lagrangian and the Klein-Gordon equation of motion are Lorentz invariant?