A Positive Energy Theorem for P(X,phi) Theories
  We describe a positive energy theorem for Einstein gravity coupled to scalar
fields with first-derivative interactions, so-called P(X,phi) theories. We
offer two independent derivations of this result. The first method introduces
an auxiliary field to map the theory to a lagrangian describing two canonical
scalar fields, where one can apply a positive energy result of Boucher and
Townsend. The second method works directly at the P(X,phi) level and uses
spinorial arguments introduced by Witten. The latter approach follows that of
arXiv:1310.1663, but the end result is less restrictive. We point to the
technical step where our derivation deviates from theirs. One of the more
interesting implications of our analysis is to show it is possible to have
positive energy in cases where dispersion relations following from locality and
S-Matrix analyticity are violated.
