The ground state energy per particle for infinite particle quantum systems

We give a simple proof that the ground state energy per particle for several interacting particle systems is monotone and bounded as the number of particles increases. Some of the systems for which the proof holds are anharmonic oscillator approximations to || _d ^/4 quantum fields, many body Schrödinger operators with nearest and next to nearest neighbor couplings, and systems whose energy is given by operators which are not restricted to being differential operators.Research partially supported by the National Science Foundation under grant No. MCS-77-03568