  A translation invariant Hamiltonian $H$ in the nonrelativistic quantum
electrodynamics is studied. This Hamiltonian is decomposed with respect to the
total momentum $\tot$: $$H=\int_{\BR} ^\oplus \fri(P) dP,$$ where the
self-adjoint fiber Hamiltonian $\fri(P)$ is defined for arbitrary values of
coupling constants. It is discussed a relationship between rotation invariance
of $H(P)$ and polarization vectors, and functional integral representations of
$n$ point Euclidean Green functions of $H(P)$ is given. From these, some
applications concerning with degeneracy of ground states, ground state energy
and expectation values of suitable observables with respect to ground states
are given.
