Linear and quadratic invariants for the transformed Tavis-Cummings model

In the present communication we introduce the transformed Tavis-Cummings problem as a physical model to discuss constants of the motion (invariants) for such a system. The Hamiltonian we have used can be regarded as a most general time-dependent frequency converter model. The advantage of the present work is to handle a real physical problem which represents the interaction between two coupled oscillators. In this context we obtained real and complex classes of linear and quadratic invariants. We have employed the real quadratic invariants to define a new Dirac operator, from which the wavefunction in the coherent states is obtained