Renormalized spectral zeta function and ground state of Rabi model

The renormalized spectral zeta function of the quantum Rabi Hamiltonian is considered. It is shown that the renormalized spectral zeta function converges to the Riemann zeta function as the coupling constant goes to infinity. Moreover the path measure associated with the ground state of the quantum Rabi Hamiltonian is constructed on a discontinuous path space, and several applications are shown.