Decoherence of Friedmann-Robertson-Walker geometries in the presence of massive vector fields with U(1) or SO(3) global symmetries

Abstract

Retrieval of classical behaviour in quantum cosmology is usually discussed in the framework of midisuperspace models in the presence of scalar fields and the inhomogeneous modes corresponding either to gravitational or scalar fields. In this work, we propose an alternative model to study the decoherence of homogeneous and isotropic geometries where the scalar field is replaced by a massive vector field with a global internal symmetry. We study here the cases with U(1) and SO(3) global internal symmetries. The presence of a mass term breaks the conformal invariance and allows for the longitudinal modes of the spin-1 field to be present in the Wheeler-DeWitt equation. In the case of the U(1) global internal symmetry, we have only one single "classical" degree of freedom while in the case of the SO(3) global symmetry, we are led to consider a simple two-dimensional minisuperspace model. These minisuperspaces are shown to be equivalent to a set of coupled harmonic oscillators where the kinetic term of the longitudinal modes has a coefficient proportional to the inverse of the scale factor. The conditions for a suitable decoherence process and correlations between coordinate and momenta are established. The validity of the semi-classical Einstein equations when massive vector fields (Abelian and non-Abelian) are present is also discussed. correlation conditions (36)-(38) are indeed satisfied restricted to those environment modes. Notice then that J |B ′ J | 2 4B 2 rJ = J   1 4 Ω ′ J Ω J 2 + |β J | 2 4Ω 2 J

The Adventures of Space-Time

“…[49]. Massive vector fields with global U (1) and SO(3) symmetries seem to be particularly suitable to generalize these results, given that the reduced matrix density and Wigner functional of the corresponding midisuperspace model [50] exhibit properties that closely resemble the localization process induced by the back-reaction of the massive long wavelength modes discussed in [49].…”

Scale-factor duality: a quantum cosmological approach

“…Inhomogeneous modes of dilaton and Yang-Mills elds could together drive decoherence due to their coupling. Decoherence could be also driven by massive v ector elds [18].…”

“…For the case where the dilaton has no potential, the corresponding WDW equation (18) where is a separation constant. The solution of (15) is then given by [16]: We shall now consider the situation where the dilaton potential is non-vanishing.…”

Generalized quantum mechanics of non-Abelian gauge theories

“…The wave functionals are taken to be functionals of scalar and vector potential configurations on an initial or final surface of constant time, as appropriate. 5 They are assumed to obey the operator form of the constraints π 0 = 0 and D · π = 0:…”