Relativistic Harmonic Oscillator Revisited

Understand

The familiar Fock space commonly used to describe the relativistic harmonic oscillator, for example as part of string theory, is insufficient to describe all the states of the relativistic oscillator.

• We find that there are three different vacua leading to three disconnected Fock sectors, all constructed with the same creation-annihilation operators.
• These have different spacetime geometric properties as well as different algebraic symmetry properties or different quantum numbers.
• Two of these Fock spaces include negative norm ghosts (as in string theory) while the third one is completely free of ghosts.