Title:	Sorkin-Johnston vacuum for a massive scalar field in the 2D causal diamond
Authors:	Mathur, Abhishek Surya, Sumati
Issue Date:	Aug-2019
Publisher:	American Physical Society
Citation:	Physical Review D, 2019, Vol.100, p045007
Abstract:	We study the massive scalar field Sorkin-Johnston (SJ) Wightman function WS J restricted to a flat 2D causal diamond D of linear dimension L . Our approach is two-pronged. In the first, we solve the central SJ eigenvalue problem explicitly in the small mass regime, up to order (m L )4. This allows us to formally construct WS J up to this order. Using a combination of analytical and numerical methods, we obtain expressions for WS J both in the center and the corner of D , to leading order. We find that in the center, WS J is more like the massless Minkowski Wightman function W0mink than the massive one Wmmink, while in the corner it corresponds to that of the massive mirror Wmmirror. In the second part, in order to explore larger masses, we perform numerical simulations using a causal set approximated by a flat 2D causal diamond. We find that in the center of the diamond the causal set SJ Wightman function WSJ c resembles W0mink for small masses, as in the continuum, but beyond a critical value mc it resembles Wmmink, as expected. Our calculations suggest that unlike Wmmink, WS J has a well-defined massless limit, which mimics the behavior of the Pauli Jordan function underlying the SJ construction. In the corner of the diamond, moreover, WSJ c agrees with Wmmirror for all masses, and not, as might be expected, with the Rindler vacuum.
Description:	Open Access
URI:	http://hdl.handle.net/2289/7286
ISSN:	2470-0010 2470-0029 (online)
Alternative Location:	https://arxiv.org/abs/1906.07952 https://doi.org/10.1103/PhysRevD.100.045007 https://ui.adsabs.harvard.edu/abs/2019PhRvD.100d5007M/abstract
Copyright:	2019 American Physical Society
Appears in Collections:	Research Papers (TP)

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