  We investigate how a uniformly rotating frame is defined as the rest frame of
an observer rotating with constant angular velocity $\Omega$ around the $z$
axis of an inertial frame. Assuming that this frame is a Lorentz one, we second
quantize a free massless scalar field in this rotating frame and obtain that
creation-anihilation operators of the field are not the same as those of an
inertial frame. This leads to a new vacuum state --- a rotating vacuum ---
which is a superposition of positive and negative frequency Minkowski
particles. After this, introducing an apparatus device coupled linearly with
the field we obtain that there is a strong correlation between number of
rotating particles (in a given state) obtained via canonical quantization and
via response function of the rotating detector. Finally, we analyse
polarization effects in circular accelerators in the proper frame of the
electron making a connection with the inertial frame point of view.
