  We address issues with extant formulations of dissipative effects in the
effective field theory (EFT) which describes the post-Newtonian (PN) inspiral
of two gravitating bodies by (re)formulating several parts of the theory. Novel
ingredients include gauge invariant spherical fields in the radiation zone; a
system zone which preserves time reversal such that its violation arises not
from local odd propagation but rather from interaction with the radiation
sector in a way which resembles the balayage method; 2-way multipoles to
perform zone matching within the EFT action; and a double-field
radiation-reaction action which is the non-quantum version of the Closed Time
Path formalism and generalizes to any theory with directed propagators
including theories which are defined by equations of motion rather than an
action. This formulation unifies the treatment of outgoing radiation and its
reaction force. We demonstrate the theory in the scalar, electromagnetic and
gravitational cases by economizing the following: the expression for the
radiation source multipoles; the derivation of the leading outgoing radiation
and associated reaction force such that it is maximally reduced to mere
multiplication; and the derivation of the gravitational next to leading PN
order. In fact we present a novel expression for the +1PN correction to all
mass multipoles. We introduce useful definitions for multi-index summation, for
the normalization of Bessel functions and for the normalization of the
gravito-magnetic vector potential.
