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.

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Cited by in corpus (8)

• The causal set approach to quantum gravity
• Studies on the SJ Vacuum in de Sitter Spacetime
• The art of the state
• Entanglement Entropy of Causal Set de Sitter Horizons
• Sorkin-Johnston vacuum for a massive scalar field in the 2D causal diamond
• Singularity at the demise of a black hole
• Numerical Evaluation of the Causal Set Propagator in 2D Anti-de Sitter Spacetime
• On the (Non)Hadamard Property of the SJ State in a $1+1$D Causal Diamond