In a process in which a photon is annihilated (absorbed), we can think of the photon as making a transition into the vacuum state. Similarly, when a photon is created (emitted), it is occasionally useful to imagine that the photon has made a transition out of the vacuum state. An atom, for instance, can be considered to be "dressed" by emission and reabsorption of "virtual photons" from the vacuum. The vacuum state energy described by Σ k λ ⁠ ħω k / 2 ⁠ is infinite. We can make the replacement: ∑ ∑ k λ λ ⟶ ⟶ ∑ ∑ λ λ ( 1 2 π π ) 3 ∫ ∫ d 3 k = V 8 π π 3 ∑ ∑ λ λ ∫ ∫ d 3 k the zero-point energy density is: 1 V ∑ ∑ k λ λ 1 2 ℏ ℏ ω ω k = 2 8 π π 3 ∫ ∫ d 3 k 1 2 ℏ ℏ ω ω k = 4 π π 4 π π 3 ∫ ∫ d k k 2 ( 1 2 ℏ ℏ ω ω k ) = ℏ ℏ 2 π π 2 c 3 ∫ ∫ d ω ω ω ω 3 or in other words the spectral energy density of the vacuum field: ρ ρ 0 ( ω ω ) = ℏ ℏ ω ω 3 2 π π 2 c 3