  We formulate a general program for [...] analyzing continuous, differential
weak, simultaneous measurements of noncommuting observables, which focuses on
describing the measuring instrument autonomously, without states. The Kraus
operators of such measuring processes are time-ordered products of fundamental
differential positive transformations, which generate nonunitary transformation
groups that we call instrumental Lie groups. The temporal evolution of the
instrument is equivalent to the diffusion of a Kraus-operator distribution
function defined relative to the invariant measure of the instrumental Lie
group [...]. This way of considering instrument evolution we call the
Instrument Manifold Program. We relate the Instrument Manifold Program to
state-based stochastic master equations. We then explain how the Instrument
Manifold Program can be used to describe instrument evolution in terms of a
universal cover[,] the universal instrumental Lie group, which is independent
[...] of Hilbert space. The universal instrument is generically infinite
dimensional, in which situation the instrument's evolution is chaotic. Special
simultaneous measurements have a finite-dimensional universal instrument, in
which case the instrument is considered to be principal and can be analyzed
within the [...] universal instrumental Lie group. Principal instruments belong
at the foundation of quantum mechanics. We consider the three most fundamental
examples: measurement of a single observable, of position and momentum, and of
the three components of angular momentum. These measurements limit to strong
simultaneous measurements. For a single observable, this gives the standard
decay of coherence between inequivalent irreps; for the latter two, it gives a
collapse within each irrep onto the canonical or spherical phase space,
locating phase space at the boundary of these instrumental Lie groups.
