A Ground State for the Causal Diamond in 2 Dimensions

TL;DR

This paper investigates a proposed ground state for a quantum scalar field in a 2D causal diamond, revealing it matches Minkowski vacuum at the center and a mirror vacuum near corners, confirmed through numerical causal set analysis.

Contribution

It applies a new ground state proposal to a 2D causal diamond and uncovers its unique properties in different regions, contrasting with expected vacua.

Findings

Minkowski vacuum is recovered at the diamond's center.

The ground state near corners is a mirror vacuum, not Rindler.

Numerical causal set analysis confirms the theoretical results.

Abstract

We apply a recent proposal for a distinguished ground state of a quantum field in a globally hyperbolic spacetime to the free massless scalar field in a causal diamond in two-dimensional Minkowski space. We investigate the two limits in which the Wightman function is evaluated (i) for pairs of points that lie in the centre of the diamond (i.e. far from the boundaries), and (ii) for pairs of points that are close to the left or right corner. We find that in the centre, the Minkowski vacuum state is recovered, with a definite value of the infrared cutoff. Interestingly, the ground state is not the Rindler vacuum in the corner of the diamond, as might have been expected, but is instead the vacuum of a flat space in the presence of a static mirror on that corner. We confirm these results by numerically evaluating the Wightman function of a massless scalar field on a causal set corresponding to the continuum causal diamond.