Deriving on-shell open string field amplitudes without using Feynman rules.

We present a series of new gauge-invariant quantities in Witten's open string field theory. They are defined for a given set of open string states which satisfy the physical state condition around a classical solution. For known classical solutions, we demonstrate that these gauge-invariant quantities compute on-shell tree-level scattering amplitudes around the corresponding D-brane configuration. [ABSTRACT FROM AUTHOR]