  In this paper we study the question of effective field assignment to measured
or nonperturbatively calculated spectral functions. The straightforward
procedure is to approximate it by a sum of independent Breit-Wigner resonances,
and assign an independent field to each of these resonances. The problem with
this idea is that it introduces new conserved quantities in the free model (the
new particle numbers), therefore it changes the symmetry of the system. We
avoid this inconsistency by representing each quantum channel with a single
effective field, no matter how complicated the spectral function is.
Thermodynamical characterization of the system will be computed with this
representation method, and its relation to the independent resonance
approximation will be discussed.
