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Title: Scalar field green functions on causal sets
Authors: Ahmed, Nomaan S
Dowker, Fay
Surya, Sumati
Keywords: Quantum Gravity
Issue Date: Jun-2017
Publisher: IOP Publishing Ltd.
Citation: Classical and Quantum Gravity, 2017, Vol.34, p124002
Abstract: We examine the validity and scope of Johnston's models for scalar field retarded Green functions on causal sets in 2 and 4 dimensions. As in the continuum, the massive Green function can be obtained from the massless one, and hence the key task in causal set theory is to first identify the massless Green function. We propose that the 2d model provides a Green function for the massive scalar field on causal sets approximated by any topologically trivial 2-dimensional spacetime. We explicitly demonstrate that this is indeed the case in a Riemann normal neighbourhood. In 4d the model can again be used to provide a Green function for the massive scalar field in a Riemann normal neighbourhood which we compare to Bunch and Parker's continuum Green function. We find that the same prescription can also be used for de Sitter spacetime and the conformally flat patch of anti-de Sitter spacetime. Our analysis then allows us to suggest a generalisation of Johnston's model for the Green function for a causal set approximated by 3-dimensional flat spacetime.
Description: Restricted Access. An open-access version is available at (one of the alternative locations)
ISSN: 0264-9381
1361-6382 (E)
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Copyright: 2017 IOP Publishing Ltd.
Appears in Collections:Research Papers (TP)

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