Dynamics for causal sets with matter fields: A Lagrangian-based approach

TL;DR

This paper introduces a Lagrangian-based framework for modeling the dynamics of causal sets coupled with matter fields, emphasizing a covariant discretization approach for scalar, gauge, and gravitational fields.

Contribution

It generalizes previous methods by providing a continuum-inspired, covariant discretization scheme for causal set dynamics with matter fields.

Findings

Framework successfully incorporates matter fields into causal set dynamics.

Discretization preserves covariance and continuum properties.

Detailed treatment of scalar, gauge, and gravitational fields.

Abstract

We present a framework for the dynamics of causal sets and coupled matter fields, which is a simplification and generalization of an approach we recently proposed. Given a set of fields including the gravitational one, the main step in implementing our proposal consists in writing their continuum-based action using as variables for the spacetime geometry the causal order and volume element. One then discretizes the resulting expression, with a procedure designed to maintain covariance. After a discussion of the general framework, we treat in detail the case of scalar fields, Yang-Mills gauge fields and the gravitational field.