  This article is a response to the continued assumption, cited even in reports
and reviews of recent experimental breakthroughs and advances in theoretical
methods, that the antiJaynes-Cummings (AJC) interaction is an intractable
energy non-conserving component of the quantum Rabi model (QRM). We present
three key features of QRM dynamics : (a) the AJC interaction component has a
conserved excitation number operator and is exactly solvable (b) QRM dynamical
space consists of a rotating frame (RF) dominated by an exactly solved
Jaynes-Cummings (JC) interaction specified by a conserved JC excitation number
operator which generates the U(1) symmetry of RF and a correlated
counterrotating frame (CRF) dominated by an exactly solved antiJaynes-Cummings
(AJC) interaction specified by a conserved AJC excitation number operator which
generates the U(1) symmetry of CRF.
