The standard numerical approach to determining matrix elements of local
operators and width of resonances uses the finite volume dependence of energy
levels and matrix elements. Finite size corrections that decay exponentially in
the volume are usually neglected or taken into account using perturbation
expansion in effective field theory. Using two-dimensional sine-Gordon field
theory as "toy model" it is shown that some exponential finite size effects
could be much larger than previously thought, potentially spoiling the
determination of matrix elements in frameworks such as lattice QCD. The
particular class of finite size corrections considered here are mu-terms
arising from bound state poles in the scattering amplitudes. In sine-Gordon
model, these can be explicitly evaluated and shown to explain the observed
discrepancies to high precision. It is argued that the effects observed are not
special to the two-dimensional setting, but rather depend on general field
theoretic features that are common with models relevant for particle physics.
It is important to understand these finite size corrections as they present a
potentially dangerous source of systematic errors for the determination of
matrix elements and resonance widths.Comment: 26 pages, 13 eps figures, LaTeX2e fil
