Fiber Hamiltonians in non-relativistic quantum electrodynamics

A translation invariant Hamiltonian H   of non-relativistic quantum electrodynamics is studied. This Hamiltonian is decomposed with respect to the total momentum PTPT:H=∫Rd⊕H(P)dP, where the self-adjoint fiber Hamiltonian H(P)H(P) is defined for arbitrary values of coupling constants. The relationship between rotation invariance of H(P)H(P) and polarization vectors is discussed, and functional integral representations of n  -point Euclidean Green functions of H(P)H(P) are given. From these, applications into the degeneracy of ground states, ground state energy and expectation values of suitable observables with respect to ground states are given.