States of low energy in the Schwinger effect

Abstract

States of low energy in cosmology minimise the energy density when smeared in a chosen time interval. We extend such construction to generic homogeneous (possibly anisotropic) particle creation settings. Focusing on the Schwinger effect, we study the role played by the support of the smearing function and identify the vacua obtained in the limiting cases of small and large time intervals. We also analyse the spectral properties of the power spectrum and the number of created particles, which are complementary in characterising the vacuum, and investigate the multipolar contributions coming from the anisotropies.

Low-energy states and CPT invariance at the big bang

“…where we have used (27), and where the smearing has been done with a positive definite window function f 2 , along the curve of an isotropic observer. One can see that the temporal dependence term to be minimized is indeed the smeared energy density for each mode k with the appropriate factor ffiffiffiffiffi jgj p coming from the four-dimensional volume element.…”

“…However, the states of low energy depend, in general, on the choice of the smearing function. This method was recently applied to obtain physically motivated vacua in the Schwinger effect [27] and for scalar fields with Yukawa interaction [28].…”

Instantaneous vacuum and States of Low Energy for a scalar field in cosmological backgrounds

“…In this framework, the vacuum is defined as the state that minimizes the vacuum expectation value of the energy density averaged over a temporal window function supported around a wellmotivated initial time t = t 0 . This method has been successfully employed to obtain physically motivated vacua in bouncing inflationary scenarios in loop quantum cosmology [12], in a CPTsymmetric universe [13], and for the Schwinger effect [14]. Furthermore, the prescription to construct those states was recently extended in Ref.…”