Boundary one-point function, Casimir energy and boundary state formalism in D+1 dimensional QFT
Absztrakt:
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. (C) 2007 Elsevier B.V. All rights reserved.