Boundary one-point function, Casimir energy and boundary state formalism in D+1 dimensional QFT

We consider quantum field theories with boundary on a codimension one hyperplane. Using 1+1 dimensional examples, we clarify the relation between three parameters characterizing one-point functions, finite size corrections to the ground state energy and the singularity structure of scattering amplitudes, respectively. We then develop the formalism of boundary states in general D+1 spacetime dimensions and relate the cluster expansion of the boundary state to the correlation functions using reduction formulae. This allows us to derive the cluster expansion in terms of the boundary scattering amplitudes, and to give a derivation of the conjectured relations between the parameters in 1+1 dimensions, and their generalization to D+1 dimensions. We use these results to express the large volume asymptotics of the Casimir effect in terms of the one-point functions or alternatively the singularity structure of the one-particle reflection factor, and for the case of vanishing one-particle couplings we give a complete proof of our previous result for the leading behaviour