Renormalization of divergences in decoherence/purity calculations

Establish whether ultraviolet divergences that arise in decoherence or purity evolution calculations for open quantum field theories can be systematically renormalized using the standard renormalization program—i.e., via counterterms and composite-operator mixing—so that the resulting purity evolution is finite and regularization independent at each order in perturbation theory.

Background

The paper analyzes how tracing out heavy environmental fields can lead to nontrivial evolution of a system’s purity and examines under what circumstances ultraviolet divergences can appear in such decoherence calculations. Using a concrete example with derivative cubic interactions that break Lorentz invariance (distinct time and spatial couplings, κ_t ≠ κ_s), the authors show explicit UV-divergent terms arise when the regulator is removed, and they illustrate how these can be canceled via counterterms and nonlinear field redefinitions that mix operators of different dimensions.

Despite these illustrative cancellations, the authors do not provide a general proof that all UV divergences in decoherence/purity computations can be renormalized using standard techniques. Given that effective couplings generically require divergent renormalizations in other observables, they argue it is plausible that purity-related divergences can be treated similarly, but they emphasize that a formal, comprehensive renormalization proof remains to be established.