The important point of this is that the zero-point field energy H F does not affect the Heisenberg equation for a k λ since it is a c-number or constant (i.e. an ordinary number rather than an operator) and commutes with a k λ. We can therefore drop the zero-point field energy from the Hamiltonian, as is usually done. But the zero-point field re-emerges as the homogeneous solution for the field equation. A charged particle in the vacuum will therefore always see a zero-point field of infinite density. This is the origin of one of the infinities of quantum electrodynamics, and it cannot be eliminated by the trivial expedient dropping of the term Σ k λ ⁠ ħω k / 2 ⁠ in the field Hamiltonian.