  Jacobi operators appear as kinetic operators of several classes of
noncommutative field theories (NCFT) considered recently. This paper deals with
the case of bounded Jacobi operators. A set of tools mainly issued from
operator and spectral theory is given in a way applicable to the study of NCFT.
As an illustration, this is applied to a gauge-fixed version of the induced
gauge theory on the Moyal plane expanded around a symmetric vacuum. The
characterization of the spectrum of the kinetic operator is given, showing a
behavior somewhat similar to a massless theory. An attempt to characterize the
noncommutative geometry related to the gauge fixed action is presented. Using a
Dirac operator obtained from the kinetic operator, it is shown that one can
construct an even, regular, weakly real spectral triple. This spectral triple
does not define a noncommutative metric space for the Connes spectral distance.
