Coordenadas vestidas: formulação segundo a interpretação de Dirac-Feynman para a mecânica quântica e aplicações em CQED - Sousa Junior, L. B. de [UNESP] (2007)
In this work, we will study the just-introduced dressed coordinates in the path-integral approach, according to the Dirac-Feynman interpretation of quantum theory. These coordinates are introduced in the model of a harmonic oscillator coupled linearly to a set of normal modes of a massless scalar ﬁeld, and will allow a non-perturbative and uniﬁed description of an atom radiation process in an arbitrarily detuned cavity, generalizing the description according to the Jaynes-Cummings model, largely used in Cavity QED. The dressed coordinates also give a physically acceptable description of the system's vacuum-state stability, without necessity of appealing to the known rotating wave approximation. We will show that, in this model, the dressed coordinates reveal themselves through a nonorthogonal linear coordinate transformation preserving the path-integral functional measure, which makes it possible and simpliﬁes the calculations in this approach. We will also generalize the sum rules strategy, recently introduced to make calculations of transition probabilities easier. Finally, we will see that, in the limiting case of an inﬁnitely large cavity, we recover the well known exponencial rate of spontaneous decay of an atom in free space. On the other hand, for a sufﬁciently small cavity, the model says the oscillator can remain almost stable in its 1-excited state