where E 0 is an infinite negative constant. The vacuum state is defined as the state with no particle or antiparticle, i.e., a k | 0 ⟩ ⟩ = 0 and b k | 0 ⟩ ⟩ = 0 . Then the energy of the vacuum is exactly E 0. Since all energies are measured relative to the vacuum, H is positive definite. Analysis of the properties of a k and b k shows that one is the annihilation operator for particles and the other for antiparticles. This is the case of a fermion.