Bosonic Fields in Causal Set Theory

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.

30 pages, no figures

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• A Geometrical Description of Spinor Fields
• The use of test functions to help define quadratic Lagrangian on a causal set
• Restoring locality of scalar fields on a causal set by avoiding the use of d'Alembertians
• Ph.D. Thesis: Quantum Field Theory and Gravity in Causal Sets
• A note on discrete Holonomy through directed edges, with no lengths