  We outline a new programme of solving the problem of treating strong
interactions in field theories. The programme does not involve perturbation
theories and associated problems of divergences. We apply our recent idea of
treating strongly interacting liquids to field theories by showing the
equivalence of Hamiltonians of liquids and interacting fields. In this
approach, the motion of the field results in the disappearance of $n-1$
transverse modes with frequency smaller than the Frenkel frequency $\omega_{\rm
F}$, similar to the loss of two transverse modes in a liquid with frequency
$\omega<\omega_{\rm F}$. We illustrate the proposed programme with the
calculation of the energy and propagator, and show that the results can not be
obtained in perturbation theory to any finite order. Importantly, the Frenkel
energy gap $E_{\rm F}=\hbar\omega_{\rm F}$ and the associated massive Frenkel
particle naturally appear in our consideration, the result that is relevant for
current efforts to demonstrate a mass gap in interacting field theories such as
Yang-Mills theory. Notably, our mechanism involves a physically sensible
starting point in terms of real masses (frequencies) in the harmonic
non-interacting field, in contrast to the Higgs effect involving the imaginary
mass as a starting point. We further note that the longitudinal mode in our
approach remains gapless, implying that both short-range and long-range forces
with massive and massless particles naturally emerge and unify in a single
interacting field, a result not hitherto anticipated. Finally, we comment on
the relationship between our results and hydrodynamic description of the
quark-gluon plasma.
