  We give a functional integral representation of the semigroup generated by
the spin-boson Hamiltonian by making use of a Poisson point process and a
Euclidean field. We present a method of constructing Gibbs path measures
indexed by the full real line which can be applied also to more general
stochastic processes with jump discontinuities. Using these tools we then show
existence and uniqueness of the ground state of the spin-boson, and analyze
ground state properties. In particular, we prove super-exponential decay of the
number of bosons, Gaussian decay of the field operators, derive expressions for
the positive integer, fractional and exponential moments of the field operator,
and discuss the field fluctuations in the ground state.
