  This study discussed Dirac's bra-ket formalism for the identical particles
system to extend the rigged Hilbert space reformulated by R. Madrid [J. Phys.
A:Math. Gen. 37, 8129 (2004)]. The bra and ket vectors for a composite system
that form the basis of an identical particle system were reconstructed using
the tensor product of rigged Hilbert space.They were found to be characterized
in the dual spaces of the tensor product of nuclear spaces. The proofs utilized
in this paper adopt a format similar to that used in physics, yet they will be
mathematically rigorous. This formulation lays the foundation for modern
quantum theories based on perturbation theory, such as quantum statistical
mechanics and quantum field theory.
