The apparent dependence of nuclear matter observables on off-shell properties
of the two-nucleon potential is re-examined in the context of the effective
field theory (EFT) approach. Finite density (thermodynamic) observables are
invariant under field redefinitions, which extends the well-known theorem about
the invariance of S-matrix elements. Simple examples demonstrate how field
redefinitions can shift contributions between purely off-shell two-body
interactions and many-body forces, leaving both scattering and finite-density
observables unchanged. If only the transformed two-body potentials are kept,
however, the nuclear matter binding curves will depend on the off-shell part
(generating ``Coester bands''). The correspondence between field redefinitions
and unitary transformations, which have traditionally been used to generate
``phase-equivalent'' nucleon-nucleon potentials, is also demonstrated.Comment: 23 pages, RevTex, 9 ps figures, included with epsf.tex, minor change
