Tomonaga's idea of describing the one-dimensional jellium model in terms of bosons is adopted for the three-dimensional case, but worked out in a completely different way. An algorithm is given for the construction of a boson Hamiltonian that takes into account the full dynamics of the jellium model at all densities. The algorithm is applied to a reduced form of the jellium model, which has the same ground state energy as the jellium model in the high-density limit. The resulting boson Hamiltonian is compared with Sawada's Hamiltonian, which also has this ground state energy in the limit of high density. Finally, the present boson formulation is discussed briefly.