  A field theory is built for self-similar statistical systems with both
generating functional being the Mellin transform of the Tsallis exponential and
generator of the scale transformation that is reduced to the Jackson
derivative. With such a choice, the role of a fluctuating order parameter is
shown to play deformed logarithm of the amplitude of a hydrodynamic mode.
Within the harmonic approach, deformed partition function and moments of the
order parameter of lower powers are found. A set of equations for the
generating functional is obtained to take into account constraints and symmetry
of the statistical system.
