Gravity and Matter in Causal Set Theory
Jan, 2008Citations per year
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 for a set of fields is recast into a quasilocal expression that depends on pairs of causally related points and is a function of the values of in the Alexandrov set defined by those points, and whose limit as and approach a common point is . We then describe how to discretize , and use it to define a discrete action.- field theory: scalar
- gravitation: discrete
- quantum gravity
- matter: coupling
- causal set
- Klein-Gordon equation
- action: discrete
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