Gravity and Matter in Causal Set Theory

Details Gravity and Matter in Causal Set Theory Gravity and Matter in Causal Set Theory

2007-12-31

arxiv.org/abs/0801.0240v2

Class.Quant.Grav.26:075011,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, no figures; In version 2, friendlier results than in version 1 are obtained following much shorter derivations

Scientific paper

10.1088/0264-9381/26/7/075011

The goal of this paper is to propose an approach to the formulation of dynamics for causal sets and coupled matter fields. We start from the continuum version of the action for a Klein-Gordon field coupled to gravity, and rewrite it first using quantities that have a direct correspondent in the case of a causal set, namely volumes, causal relations, and timelike lengths, as variables to describe the geometry. In this step, the local Lagrangian density $L(f;x)$ for a set of fields $f$ is recast into a quasilocal expression $L_0(f;p,q)$ that depends on pairs of causally related points $p \prec q$ and is a function of the values of $f$ in the Alexandrov set defined by those points, and whose limit as $p$ and $q$ approach a common point $x$ is $L(f;x)$. We then describe how to discretize $L_0(f;p,q)$, and use it to define a discrete action.

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