  The complete expression for the intensity in pseudo-scalar meson
photoproduction with a polarized beam, target, and recoil baryon is derived
using a density matrix approach that offers great economy of notation. A
Cartesian basis with spins for all particles quantized along a single
direction, the longitudinal beam direction, is used for consistency and clarity
in interpretation. A single spin-quantization axis for all particles enables
the amplitudes to be written in a manifestly covariant fashion with simple
relations to those of the well-known CGLN formalism. Possible sign
discrepancies between theoretical amplitude-level expressions and
experimentally measurable intensity profiles are dealt with carefully. Our
motivation is to provide a coherent framework for coupled-channel partial-wave
analysis of several meson photoproduction reactions, incorporating recently
published and forthcoming polarization data from Jefferson Lab.
