  In this article, I have considered a real scalar field theory and able to
show that under Bogoliubov transformation in infinite volume limit or
thermodynamic limit the transformed Hamiltonian no longer invariant under U(1)
action defined appropriately as it was before doing transformation. We also
have checked this fact by looking at the correlation functions under the action
of U(1) group. We suitably defined field operators that are associated with
particle production phenomena then we can also show that correlation functions
of such field operators also don't follow U(1) invariance, shown in this
article. This is a consequence of non-invariance of transformed Hamiltonian
under U(1) action. Since, we know Bogoliubov transformation in curved spacetime
is equivalent to doing a coordinate transformation, therefore this result
directly shows the phenomena of particle production under the affect of gravity
since changing coordinate is equivalent to turn on gravity according to
Einstein's equivalence principle in GR. I also show that particle production
does not take place out of vacuum state but it can happen out of other
many-particle states and vacuum state is not an eigenvector of Hamltonian
operator in transformed Fock space and vacuum state does not remain vacuum
state under time evolution.
