The Sorkin–Johnston state in a patch of the trousers spacetime

Abstract

A quantum scalar field in a patch of a fixed, topology-changing, 1 + 1 dimensional "trousers" spacetime is studied using the Sorkin-Johnston formalism. The isometry group of the patch is the dihedral group, the symmetry group of the square. The theory is shown to be pathological in a way that can be interpreted as the topology change giving rise to a divergent energy, in agreement with previous results. In contrast to previous results, it is shown that the infinite energy is localised not only on the future light cone of the topology changing singularity, but also on the past cone, due to the time reversal symmetry of the Sorkin-Johnston state.arXiv:1609.03573v2 [gr-qc]

The art of the state

“…The SJ state has also been investigated in other spacetime regions of interest, including diamond regions in 1 + 1-dimensional Minkowski spacetime 55 and a patch of the 'pair of trousers' 1 + 1dimensional topology-changing spacetime, 56 studying the massless scalar field in each case. For the diamond, it was found that the SJ two-point function approaches the Minkowski form when the two points are both near the centre of the diamond and close to one another, relative to the overall length scale of the diamond.…”

“…The trousers case is interesting because it not globally hyperbolic; here, specific non-Hadamard behaviour (divergent energy density) is found, which is attributed to singular behaviour where the metric degenerates. 56…”

Sorkin-Johnston vacuum for a massive scalar field in the 2D causal diamond

“…The SJ prescription provides an observer independent mode decomposition φ defined in a compact globally hyperbolic spacetime region [1,2,3,5,6,8,9,10]. Instead of an equal time commutation relation, it uses the covariant Peierls bracket φ(X), φ(X ) = i∆(X, X ), (5) where the Pauli Jordan function is given by…”

“…As a result there are very few cases in which W SJ has been obtained explicitly. These include the massless free scalar SJ vacuum in a 2D flat causal diamond [3,4], a patch of trousers spacetime [5] and the ultrastatic slab spacetime [6]. In this work, we study the SJ vacuum for a massive free scalar field in the 2D flat causal diamond D of length 2L, both in the continuum and on a causal set C D obtained from sprinkling into D.…”

High performance algorithms for quantum gravity and cosmology

“…One attempt is the Classical Sequential Growth model[75], which provides a stochastic growth model for causal sets. Subsequent work has examined the dynamics of scalar fields propagating across causal sets[76][77][78][79], including those with variable topology[80]. Other recent work uses a top-down approach with Monte Carlo dynamics to evaluate the gravitational partition function furnished by the Einstein-Hilbert action S EH ,…”