  Traditionally, Quantum Field Theory (QFT) treats particle excitations as
point-like objects, which is the source of ubiquitous divergences. We
demonstrate that a minimal modification of QFT with finite volume particles may
cure QFT of divergences and illuminate the physics behind the mathematical
construct of our theories. The method allows for a non-perturbative treatment
of the free field and self-interacting theories (though extensions to all
interacting field theories might be possible). In particular,
non-perturbatively defined mass is finite. When applied to the standard model
Higgs mechanism, the method implies that a finite range of parameters allows
for creation of a well defined Higgs particle, whose Compton wavelength is
larger than its physical size, in the broken symmetry phase (as small
oscillations around the vacuum). This has profound consequences for Higgs
production at the LHC. The parameter range in which the Higgs excitation with
the mass of 125 GeV behaves as a proper particle is very restricted.
