A Hamiltonian with Linear Kinetic Energy for Systems of Many Bodies

A proper quantum-mechanical hamiltonian should have a single time variable and a single energy, but a corresponding Lorentz invariant expression for the rest energy has so far not been found. In this paper, an approximately Lorentz invariant form incorporating the potential energy of interactions between particles is put into an equivalent linear form by the use of Clifford algebra. Some of the properties of the resulting many-body hamiltonian are set out and some applications to molecular structure are indicated.