  This work deals with form factors of the energy-momentum tensor (EMT) of
spin-0 particles and the unknown particle property D-term related to the EMT,
and is divided into three parts.
  The first part explores free, weakly and strongly interacting theories to
study EMT form factors with the following findings. (i) The free Klein-Gordon
theory predicts for the D-term D = -1. (ii) Even infinitesimally small
interactions can drastically impact D. (iii) In strongly interacting theories
one can encounter large negative D though notable exceptions exist, which
includes Goldstone bosons of chiral symmetry breaking. (iv) Contrary to common
belief one cannot arbitrarily add "total derivatives" to the EMT. Rather the
EMT must be defined in an unambiguous way.
  The second part deals with the interpretation of EMT form factors in terms of
3D-densities with following results. (i) The 3D-density formalism is internally
consistent. (ii) The description is subject to relativistic corrections which
are acceptably small in phenomenologically relevant situations including
nucleon and nuclei. (iii) The free field result D=-1 persists when a spin-0
boson is not point-like but "heuristically given some internal structure."
  The third part investigates the question, whether such "giving of an extended
structure" can be implemented dynamically, and has the following insights. (i)
We construct a consistent microscopic theory which, in a certain parametric
limit, interpolates between extended and point-like solutions. (ii) This theory
is exactly solvable which is rare in 3+1 dimensions, admits non-topological
solitons of Q-ball-type, and has a Gaussian field amplitude. (iii) The
interaction of this theory belongs to a class of logarithmic potentials which
were discussed in literature, albeit in different contexts including beyond
standard model phenomenology, cosmology, and Higgs physics.
