  In conventional superconductors the Cooper pairs have a zero center of mass
momentum. In this paper we present a theory of superconducting states where the
Cooper pairs have a nonzero center of mass momentum, inhomogeneous
superconducting states known as a pair-density-waves (PDW) states. We show that
in a system of spin-1/2 fermions in 2 dimensions in an electronic nematic spin
triplet phase where rotational symmetry is broken both in real and in spin
space PDW phases arise naturally in a theory that can be analyzed using
controlled approximations. We show that several superfluid phases that may
arise in this phase can be treated within a controlled BCS mean field theory,
with the strength of the spin-triplet nematic order parameter playing the role
of the small parameter of this theory. We find that in a spin-triplet nematic
phase, in addition of a triplet $p$-wave and spin-singlet $d$-wave (or $s$
depending on the nematic phase) uniform superconducting states, it is also
possible to have a $d$-wave (or $s$) PDW superconductor. The PDW phases found
here can be either unidirectional, bidirectional or tridirectional depending on
the spin-triplet nematic phase and which superconducting channel is dominant.
In addition, a triple-helix state is found in a particular channel. We show
that these PDW phases are present in the weak coupling limit, in contrast to
the usual Fulde-Ferrell-Larkin-Ovchinnikov phases which require strong coupling
physics in addition to a large magnetic field (and often both).
