The system of N-nonrelativistic spineless particles minimally coupled to a massless quantized radiation field with an ultraviolet cutoff is considered. The Hamiltonian of the system is defined for arbitrary coupling constants in terms of functional integrals. It is proved that the ground state of the system with a class of external potentials, if they exist, is unique. Moreover an expression of the ground state energy is obtained and it is shown that the ground state energy is a monotonously increasing, concave, and continuous function with respect to the square of a coupling constant.
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