  Effective field theories describing gravity coupled to matter are
investigated, allowing for operators of arbitrary mass dimension. Terms
violating local Lorentz and diffeomorphism invariance while preserving internal
gauge symmetries are included. The theoretical framework for violations of
local Lorentz and diffeomorphism invariance and associated conceptual issues
are discussed, including transformations in curved and approximately flat
spacetimes, the treatment of various types of backgrounds, the implications of
symmetry breaking, and the no-go constraints for explicit violation in Riemann
geometry. Techniques are presented for the construction of effective operators,
and the possible terms in the gravity, gauge, fermion, and scalar sectors are
classified and enumerated. Explicit expressions are obtained for terms
containing operators of mass dimension six or less in the effective action for
General Relativity coupled to the Standard Model of particle physics. Special
cases considered include Einstein-Maxwell effective field theories and the
limit with only scalar coupling constants.
