  The only efficient and robust method of generating consistent initial data in
general relativity is the conformal technique initiated by Lichnerowicz and
perfected by York. In the spatially compact case, the complete scheme consists
of the Arnowitt-Deser-Misner (ADM) Hamiltonian and momentum constraints, the
ADM Euler-Lagrange equations, York's constant-mean-curvature (CMC) condition,
and a lapse-fixing equation (LFE) that ensures propagation of the CMC condition
by the Euler-Lagrange equations. The Hamiltonian constraint is rewritten as the
Lichnerowicz-York equation for the conformal factor (psi) of the physical
metric (psi)^4(g_{ij}) given an initial unphysical 3-metric (g_{ij}). The CMC
condition and LFE introduce a distinguished foliation (definition of
simultaneity) on spacetime, and separate scaling laws for the canonical momenta
and their trace are used. In this article, we derive all these features in a
single package by seeking a gauge theory of geometrodynamics (evolving
3-geometries) invariant under both three-dimensional diffeomorphisms and
volume-preserving conformal transformations.
