  It is shown that a unitary translationally invariant field theory in (1+1)
dimensions satisfying isotropic scale invariance, standard assumptions about
the spectrum of states and operators and the requirement that signals propagate
with finite velocity possesses an infinite dimensional symmetry given by one or
a product of several copies of conformal algebra. In particular, this implies
presence of one or several Lorentz groups acting on the operator algebra of the
theory.
