transformation \[equations (\[back\_6\])-(\[back\_7\_3\])\]. The method is based on the correspondence between this model and the dynamics of a Dirac particle subject to an appropriate electromagnetic field configuration. Once the correspondence is established, the Lorentz covariance of the Dirac equation will be exploited to reach the desired solutions.

Section \[secc:Dirac\] is devoted to the correspondence between the relativistic and quantum optical models. We first introduce the Dirac equation for a charged particle subject to an external electromagnetic field and then present a particular field configuration where the evolution of the Dirac particle mimics the system under the driven Jaynes–Cummings Hamiltonian. In Section \[secc:Lorentz\] we obtain the eigenvalues and eigenstates of the Dirac equation; by considering the relativistic invariants of the electromagnetic field, they are shown to display two distinct behaviours which are connected to particularly simple physical scenarios through Lorentz transformations. In Section \[secc:Jaynes\_cummings\] we return to the quantum optical model and review the solutions in this context, where the relation between Lorentz and squeezing transformations is discussed. Section \[secc:conclusion\] is left for conclusions.

Correspondence to a relativistic system {#secc:Dirac}
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The dynamics of a spin-1/2 particle of mass $m$ and charge $e$ in the presence of an external electromagnetic field 