Dressed particles from the star-unitary transformation: Markovian dynamics

We construct the dressed particle formulation of a particle-field interaction model based on the theory of star-unitarity transformations. When the system is integrable in Poincaré’s sense, the description is initiated by a unitary transformation that diagonalizes the Hamiltonian. When the system is non-integrable, resonant poles give rise to non-analyticity in the coupling constant for dressed observables. This can be regularized to produce a star-unitary transformation that serves as an extension of the unitary transformation. On the level of correlation functions, we show that for high temperature the transformation effectively gives rise to white noise correlations with purely exponential decay. The logarithmic divergence in the bare momentum autocorrelation function associated with nonwhite noise is thus avoided. However, we find that the previously proposed maximal regularization scheme is not applicable to the low temperature regime since it neglects the contribution from the low frequency domain of the spectrum that becomes important in this regime. We discuss the root of the problem and suggest a plausible way of correcting it.