Bosonic Fields in Causal Set Theory

TL;DR

This paper develops a covariant Lagrangian formulation for scalar and gauge fields within causal set theory by minimizing variations of field expressions over Alexandrov sets, advancing the discrete approach to quantum field theory.

Contribution

It introduces a novel method to define covariant Lagrangians for scalar and gauge fields in causal set theory using Alexandrov sets and variation minimization.

Findings

Defined covariant Lagrangians for scalar and gauge fields in causal sets.

Established a variational principle based on Alexandrov sets.

Provided a framework for discrete quantum field theories.

Abstract

In this paper we will define a Lagrangian for scalar and gauge fields on causal sets, based on the selection of an Alexandrov set in which the variations of appropriate expressions in terms of either the scalar field or the gauge field holonomies around suitable loops take on the least value. For these fields, we will find that the values of the variations of these expressions define Lagrangians in covariant form.