  We develop a new transformation theory in quantum physics, where the
transformation operators, defined in the infinite dimensional Hilbert space,
have right-unitary inverses only. Through several theorems, we discuss the
properties of state space of such operators. As one application of the
right-unitary transformation (RUT), we show that using the RUT method, we can
solve exactly various interactions of many-level atoms with quantized radiation
fields, where the energy of atoms can be two levels, three levels in Lambda, V
and equiv configurations, and up to higher (>3) levels. These interactions have
wide applications in atomic physics, quantum optics and quantum electronics. In
this paper, we focus on two typical systems: one is a two-level generalized
Jaynes-Cummings model, where the cavity field varies with the external source;
the other one is the interaction of three-level atom with quantized radiation
fields, where the atoms have Lambda-configuration energy levels, and the
radiation fields are one-mode or two-mode cavities.
