Gravitationally induced decoherence of a scalar field: investigating the one-particle sector and its interplay with renormalisation

TL;DR

This work tackles gravitationally induced decoherence for a scalar field by focusing on the one-particle sector and performing an on-shell, UV renormalisation directly at the level of the underlying effective quantum field theory, prior to Markov and rotating-wave approximations.By deriving both non-covariant and covariant Feynman rules, identifying vacuum self-energy divergences with UV poles, and implementing on-shell renormalisation, the authors show that vacuum (temperature-independent) contributions in the Lamb-shift and dissipator are absorbed, leaving a renormalised master equation sensitive only to thermal effects.Applying the Markov and post-trace rotating-wave approximations then yields a Lindblad-form dynamics in relevant regimes, with explicit ultra-relativistic and non-relativistic limits; in particular, the ultra-relativistic limit yields a simple decoherence rate and a direct link to neutrino-oscillation decoherence models.The results illuminate how renormalisation alters the physical content of decoherence predictions, enable clean comparisons with previous field-theoretic and quantum-mechanical models, and pave the way for incorporating wave-packet descriptions and fermionic cases in future work.

Abstract

We investigate the one-particle sector for the field-theoretical model of gravitationally induced decoherence for a scalar field in [1] with a special focus on the renormalisation of the one-particle master equation. In contrast to existing models in the literature, where the renormalisation is usually performed after the Markov and rotating wave approximation and often only for certain limits such as the non- or ultra-relativistic limit, here we apply the renormalisation directly after the one-particle projection. With this strategy, we show that UV-divergent contributions in the one-particle master equation can be identified with the vacuum contributions in the self-energy of the scalar field in the effective quantum field theory and depending on the chosen one-particle projection method, its vacuum bubbles, while the additional thermal contributions in the self-energy are all UV-finite. To obtain the renormalised one-particle master equation, we use an on-shell renormalisation procedure of the underlying effective QFT. We then apply the Markov and rotating wave approximation, specifying a condition under which the Markov approximation can be applied in the case of the ultra-relativistic limit. We compare our results with those available in the literature. This includes an analysis of two different kinds of one-particle projections, a comparison of the application and effects of renormalisation of quantum mechanical and field theoretical models, the non-relativistic and ultra-relativistic limits of the renormalised one-particle master equations, and a comparison with a quantum mechanical toy model for gravitationally induced decoherence in the context of neutrino oscillations.