  The goal of the present note is to understand whether it is possible to
define interacting quantum field theory in global anti de Sitter space-time
with Lorentzian signature, in its covering space-time (whose time coordinate is
not periodic) and in its Poincare patch. We show that in global anti de Sitter
space-time there are certain problems to define quantum field theory properly.
This is due to an additional UV singularity of the Feynman propagator which is
sitting on the light-cone emanating from the antipodal point of the source.
There is no such singularity in flat space-time. At the same time quantum field
theory in Poincare region of the AdS space-time can be well defined and is
related to the one in Euclidean AdS via the analytical continuation. In
principle one can also define and analytically continue quantum field theory in
the covering anti de Sitter space-time. However, to do that one has to use an
unusual $i\epsilon$-prescription in the Feynman propagator, which cannot be
used in loop calculations in non-stationary situations.
