ABSTRACT
As position is no longer a quantum observable but free particles do not seem to be in contradiction with relativistic invariance. For a real scalar field, a particle is its own antiparticle and this description is perhaps somewhat unfamiliar. It is the property of the harmonic oscillator that its energy is linear in the occupation number, which makes the field theory interpretation in terms of particles possible. Interactions between the particles are simply introduced by modifying the Klein–Gordon equation to have nonlinear terms, after which in general the different Fourier components no longer decouple. Field theory thus seems to be nothing but the quantum mechanics of an infinite number of degrees of freedom. As each zero-point energy is nonzero, the energy of the vacuum in field theory seems to be infinite.
