  The relativistic quantum field theory is the unique theory that combines the
relativity and quantum theory and is invariant under the Poincar\'e
transformation. The ground state, vacuum, is singlet and one particle states
are transformed as elements of irreducible representation of the group. The
covariant one particles are momentum eigenstates expressed by plane waves and
extended in space. Although the S-matrix defined with initial and final states
of these states hold the symmetries and are applied to isolated states,
out-going states for the amplitude of the event that they are detected at a
finite-time interval T in experiments are expressed by microscopic states that
they interact with, and are surrounded by matters in detectors and are not
plane waves. These matter-induced effects modify the probabilities observed in
realistic situations. The transition amplitudes and probabilities of the events
are studied with the S-matrix, $S[\text T]$, that satisfies the boundary
condition at T. Using $S[\text T]$, the finite-size corrections of the form of
${1/\text T}$ are found. The corrections to the Fermi's golden rule become
larger than the original values in some situations for light particles. They
break Lorentz invariance even in high energy region of short de Broglie wave
lengths.
