Field redefinitions at finite density Original Research Article

The apparent dependence of nuclear matter observables on off-shell properties of the two-nucleon potential is re-examined in the context of effective field theory (EFT). 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.