  We analyze the transformation of quantum fields under conformal coordinate
transformations from inertial to accelerated frames, in the simple case of
scalar massless fields in a two-dimensional spacetime, through the
transformation of particle number and its spectral density. Particle number is
found to be invariant under conformal coordinate transformations to uniformly
accelerated frames, which extends the property already known for vacuum.
Transformation of spectral density of particle number exhibits a redistribution
of particles in the frequency spectrum. This redistribution is determined by
derivatives of phase operators with respect to frequency, that is by time and
position operators defined in such a manner that the redistribution of
particles appears as a Doppler shift which depends on position in spacetime, in
conformity with Einstein equivalence principle.
