Discrete wave operator for causets

Joseph Samuel

Joseph Samuel is an Editorial Board member of Classical and Quantum Gravity and a Professor at the Raman Research Institute, Bangalore, India

This paper leads to a discrete action functional on causets.

Lisa Glaser presents some tidy results in the definition of the discrete d’Alembertian operator on a causet in any dimension.

The causet approach to quantum gravity was pioneered by Rafael Sorkin in the 1980s. It approximates the space-time continuum by a discrete structure–a set with a partial order. The causet approach is marked by its minimalist philosophy, capturing Lorentzian manifolds in a discrete net with just two ingredients: the partial ordering of elements and the number of causet elements.

Given this sparse structure, how does one do physics with causets and address problems of quantisation? Researchers over the globe have made much progress in this area. One of the most basic differential operators for physics is the wave operator. This paper by Lisa Glaser gives a closed form for the discrete wave operator on a Causet in any dimension, building on earlier work in lower dimensions. Knowing the d’Alembertian permits us to define the scalar curvature by letting the operator act on a constant scalar field. This gives us a discrete version of the Einstein–Hilbert action for a causet.

The exposition in this paper keeps the bigger picture firmly in view. While the article is of interest to specialists in causets, a general reader will also be well rewarded with an easy entry into the current state of the art in this important area. The clear exposition of the background and main issues involved is an invitation to plunge in. Do so!

Read the full article: Class. Quantum Grav. 31 095007

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  1. Pingback: 2016 Bergmann Thesis Prize winner: Lisa Glaser | CQG+

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