  We investigate the self-organizing nature of relativistic quantum field
theory in terms of canonical transformation and duality presenting simple but
explicit examples of $(\phi^4)_{1+1}$ and $(\phi^6)_{1+1}$ theories. Our
purpose is fulfilled by applying the oscillator representation (OR) method
which allows us to convert the original strong interaction theory into a weekly
interacting quasiparticle theory that is equivalent to the original theory. We
discuss advantages of the OR method and compare the results with what was
already obtained by the method of Gaussian effective potential (GEP) and the
Hartree approximation (HA). While we confirm that the GEP results are identical
to the Hartree results for the ground state energy, we found that the OR method
gives the quasiparticle mass different from the GEP and HA results. In our
examples, the self-organizing nature is revealed by the vacuum energy density
that gets lowered when the quasiparticles are formed. In the $(\phi^6)_{1+1}$
theory, we found two physically meaningful duality-related quasiparticle
solutions which have different symmetry properties under the transition of
quasiparticle field $\Phi \to -\Phi$. However, these two quasiparticle
solutions yield the identical effective potential in the strong coupling limit
of the original theory.
