Quantum to classical transition in quantum field theory

TL;DR

This paper investigates the quantum to classical transition in quantum field theory, analyzing decoherence and the emergence of classical behavior in various spacetime geometries and models, including quantum gravity and cosmology.

Contribution

It extends the influence functional formalism to quantum field theory in curved spacetime, providing new insights into decoherence, the classical limit, and quantum fluctuations in gravitational contexts.

Findings

Decoherence is effective for long-wavelength modes beyond the Hubble radius.

Derived master equations and diffusion coefficients for quantum fields in flat and curved spacetimes.

Identified conditions under which semiclassical approximation holds in cosmological models.

Abstract

We study the quatum to classical transition process in the context of quantum field theory. Extending the influence functional formalism of Feynman and Vernon, we study the decoherence process for self-interacting quantum fields in flat space. We also use this formalism for arbitrary geometries to analyze the quantum to classical transition in quantum gravity. After summarizing the main results known for the quantum Brownian motion, we consider a self-interacting field theory in Minkowski spacetime. We compute a coarse grained effective action by integrating out the field modes with wavelength shorter than a critical value. From this effective action we obtain the evolution equation for the reduced density matrix (master equation). We compute the diffusion coefficients for this equation and analyze the decoherence induced on the long-wavelength modes. We generalize the results to the case of a conformally coupled scalar field in de Sitter spacetime. We show that the decoherence is effective as long as the critical wavelength is taken to be not shorter than the Hubble radius. On the other hand, we study the classical limit for scalar-tensorial models in two dimensions. We consider different couplings between the dilaton and the scalar field. We discuss the Hawking radiation process and, from an exact evaluation of the influence functional, we study the conditions by which decoherence ensures the validity of the semiclassical approximation in cosmological metrics. Finally we consider four dimensional models with massive scalar fields, arbitrary coupled to the geometry. We compute the Einstein-Langevin equations in order to study the effect of the fluctuations induced by the quantum fields on the classical geometry.