Gravity and Matter in Causal Set Theory

Jan, 2008
21 pages
Published in:
  • Class.Quant.Grav. 26 (2009) 075011
e-Print:

Citations per year

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Abstract: (arXiv)
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)L(f/x) for a set of fields ff is recast into a quasilocal expression L0(f/p,q)L_0(f/p,q) that depends on pairs of causally related points pqp \prec q and is a function of the values of ff in the Alexandrov set defined by those points, and whose limit as pp and qq approach a common point xx is L(f/x)L(f/x). We then describe how to discretize L0(f/p,q)L_0(f/p,q), and use it to define a discrete action.
  • field theory: scalar
  • gravitation: discrete
  • quantum gravity
  • matter: coupling
  • causal set
  • Klein-Gordon equation
  • action: discrete