An Expression of the Ground State Energy of the Spin-Boson Model

An expression of the ground state energyESBof the spin-boson HamiltonianHSBis considered. The expression in the cases of both massive and massless bosons is given by a nonperturbative method. By using the expression, we show a necessary and sufficient condition with respect to a parameterG∈[−1, 0] such that a formula withGattains toESB.