All of these postulates continue to hold in relativistic QFT, except that the time-evolution operation is no longer defined by the Schrodinger equation with a nonrelativistic Hamiltonian.

The only one that requires significant new elaboration in the relativistic context is the existence of an inner product. In nonabelian gauge theory, it often a useful calculational trick to formally expand your Hilbert space to a larger state space that includes negative-norm "ghosts." Such a state space is no longer a Hilbert space because its sesquisymmetric bilinear form is no longer positive definite, and is therefore no longer an inner product. But the key point is that you never have to introduce ghosts; they are merely a useful calculation trick, but do not physically exist. You can always do any calculation without invoking ghosts; See here.

All of these postulates continue to hold in relativistic QFT, except that the time-evolution operator is no longer defined by the Schrodinger equation with a nonrelativistic Hamiltonian.

The only one that requires significant new elaboration in the relativistic context is the existence of an inner product. In nonabelian gauge theory, it often a useful calculational trick to formally expand your Hilbert space to a larger state space that includes negative-norm "ghosts." Such a state space is no longer a Hilbert space because its sesquisymmetric bilinear form is no longer positive definite, and is therefore no longer an inner product. But the key point is that you never have to introduce ghosts; they are merely a useful calculation trick, but do not physically exist. You can always do any calculation without invoking ghosts; See here.

All of these postulates continue to hold in relativistic QFT, except that the time-evolution operation is no longer defined by the Schrodinger equation with a nonrelativistic Hamiltonian.

The only one that requires significant new elaboration in the relativistic context is the existence of an inner product. In nonabelian gauge theory, it often a useful calculational trick to formally expand your Hilbert space to a larger state space that includes negative-norm "ghosts." Such a state space is no longer a Hilbert space because its sesquisymmetric bilinear form is no longer positive definite, and is therefore no longer an inner product. But the key point is that you never have to introduce ghosts, they are merely a useful calculation trick but do not actually exist. You can always do any calculation without invoking ghosts; See here.

All of these postulates continue to hold in relativistic QFT, except that the time-evolution operation is no longer defined by the Schrodinger equation with a nonrelativistic Hamiltonian.

The only one that requires significant new elaboration in the relativistic context is the existence of an inner product. In nonabelian gauge theory, it often a useful calculational trick to formally expand your Hilbert space to a larger state space that includes negative-norm "ghosts." Such a state space is no longer a Hilbert space because its sesquisymmetric bilinear form is no longer positive definite, and is therefore no longer an inner product. But the key point is that you never have to introduce ghosts; they are merely a useful calculation trick, but do not physically exist. You can always do any calculation without invoking ghosts; See here.