  Recent advances in non-critical string theory allow a unique continuation,
preserving conformal invariance, of critical Polyakov string amplitudes to
off-shell momenta. These continuations possess unusual, apparently stringy,
characteristics, which are unlikely to be reproduced in a string field theory.
Thus our results may be an indication that some fundamentally new formulation,
other than string field theory, will be required to extend our understanding of
critical strings beyond the Polyakov path integral. Three-point functions are
explicitly calculated. The tree-level effective potential is computed for the
tachyon. (This preprint includes some computations used to arrive at results
mentioned in hep-th/9211016.)
