  We reexamine the invariance of two-photon transition matrix elements and
corresponding two-photon Rabi frequencies under the "gauge" transformation from
the length to the velocity gauge. It is shown that gauge invariance, in the
most general sense, only holds at exact resonance, for both one-color as well
as two-color absorption. The arguments leading to this conclusion are supported
by analytic calculations which express the matrix elements in terms of
hypergeometric functions, and ramified by a "master identity" which is
fulfilled by off-diagonal matrix elements of the Schroedinger propagator under
a the transformation from the velocity to the length gauge. The study of the
gauge dependence of atomic processes highlights subtle connections between the
concept of asymptotic states, the gauge transformation of the wave function,
and infinitesimal damping parameters for perturbations and interaction
Hamiltonians that switch off the terms in the infinite past and future [of the
form exp(-epsilon * | t |)]. We include a pertinent discussion.
