  A new localization scheme for Klein-Gordon particle states is introduced in
the form of general space and time operators. The definition of these operators
is achieved by establishing a second quantum field in the momentum space of the
standard field we want to localize (here Klein-Gordon field). The motivation
for defining a new field in momentum space is as follows. In standard field
theories one can define a momentum (and energy) operator for a field excitation
but not a general position (and time) operator because the field satisfies a
differential equation in position space and, through its Fourier transform, an
algebraic equation in momentum space. Thus, in a field theory which does the
opposite, namely it satisfies a differential equation in momentum space and an
algebraic equation in position space, we will be able to define a position and
time operator. Since the new field lives in the momentum space of the
Klein-Gordon field, the creation/annihilation operators of the former, which
build the new space and time operators, reduce to the field operators of the
latter. As a result, particle states of Klein-Gordon field are eigenstates of
the new space and time operators and therefore localized on a space-time
described by their spectrum. Finally, we show that this space-time is flat
because it accommodates the two postulates of special relativity.
Interpretation of special relativistic notions as inertial observers and proper
acceleration in terms of the new field is also provided.
