Quantum Field Theory In Curved Spacetime Research Articles

Borel resummation of secular divergences in stochastic inflation

We make use of Borel resummation to extract the exact time dependence from the divergent series found in the context of stochastic inflation. Correlation functions of self-interacting scalar fields in de Sitter spacetime are known to develop secular IR divergences via loops, and the first terms of the divergent series have been consistently computed both with standard techniques for curved spacetime quantum field theory and within the framework of stochastic inflation. We show that Borel resummation can be used to interpret the divergent series and to correctly infer the time evolution of the correlation functions. In practice, we adopt a method called Borel-Padé resummation where we approximate the Borel transformation by a Padé approximant. We also discuss the singularity structures of Borel transformations and mention possible applications to cosmology.

Quantum Signatures of Black Hole Mass Superpositions.

We present a new operational framework for studying "superpositions of spacetimes," which are of fundamental interest in the development of a theory of quantum gravity. Our approach capitalizes on nonlocal correlations in curved spacetime quantum field theory, allowing us to formulate a metric for spacetime superpositions as well as characterizing the coupling of particle detectors to a quantum field. We apply our approach to analyze the dynamics of a detector (using the Unruh-deWitt model) in a spacetime generated by a Banados-Teitelboim-Zanelli black hole in a superposition of masses. We find that the detector exhibits signatures of quantum-gravitational effects corroborating and extending Bekenstein's seminal conjecture concerning the quantized mass spectrum of black holes in quantum gravity. Crucially, this result follows directly from our approach, without any additional assumptions about the black hole mass properties.

Perturbative semiclassical approximation in the uniform curvature gauge

Fluctuations in the scalar field considered in curved spacetime necessarily induce fluctuations in the metric. Quantum treatment of the simultaneously fluctuating field and metric system may be distinguished from the ordinary quantum field theory in curved spacetime (QFCS) treatment. We call this approach the perturbative semiclassical approximation. When we consider the fluctuating metric we have the freedom to choose a gauge. By a proper choice of gauge we show that the perturbative semiclassical approximation can be treated as simply as the QFCS approximation, and can be regarded as more consistent and general than the latter. By neglecting the metric fluctuations the equation for the perturbed scalar field can be considered to be truncated. However, in a couple of special expansion stages the contributions from the metric fluctuations exactly cancel out. This may confirm why the conventional QFCS applied to such special expansion stages is not inconsistent. We derive the perturbation equation in a conventional way starting from Einstein's equation. Consequential results are summarized in a self-contained manner.

Quantum field theory in curved space-time as thermo field dynamics

The strong analogy between states defined in the context of quantum field theory in curved space-time (QFT-CST) and the ones defined in the thermo field dynamics (TFD) of Takahashi and Umezawa [1] is shown. This analogy is useful in order to introduce the entropy operator in CST in the same way as in TFD. When the extremum condition in the thermodynamical potential is imposed, a family of Bogoliubov transformations that give us a planckian spectrum is found, even in “pathological” cases such as the minimally coupled scalar field.

Momentum space techniques for curved space–time quantum field theory

A momentum space formulation of curved space–time quantum field theory is presented. Such a formulation allows the riches of momentum space calculational techniques already existing in nuclear physics to be exploited in the application of quantum field theory to cosmology and astrophysics. It is demonstrated that one such technique can allow exact, or very accu­rate approximate, results to be obtained in cases which are intractable in coordinate space. An efficient method of numerical solution is also described.