Probabilistic solutions of generalised birth and death equations and applications to field theory

The paper concerns probabilistic solutions to equations describing non-relativistic quantum 'electrodynamical' systems. The solutions involve, besides the usual diffusion processes, birth and death processes corresponding to the 'photon number' variables. The forced harmonic oscillator and the field-particle interaction is considered. Inequalities are stated, and an upper bound is found for the ground-state energy of systems composed of a non-relativistic particle interacting with a field. The result is general and it is applied as an example to the polaron problem. (U.K.)