Gauge Fields in Causal Set Theory

Abstract

This is the second paper in a series on the dynamics of matter fields in the causal set approach to quantum gravity. We start with the usual expression for the Lagrangian of a charged scalar field coupled to a SU(n) Yang-Mills field, in which the gauge field is represented by a connection form, and show how to write it in terms of holonomies between pairs of points, causal relations, and volumes or timelike distances, all of which have a natural correspondence in the causal set context. In the second part of the paper we present an alternative model, in which the gauge field appears as the result of a procedure inspired by the Kaluza-Klein reduction in continuum field theory, and the dynamics can be derived simply using the gravitational Lagrangian of the theory.

11 pages, no figures

References in corpus (2)

• The causal set approach to quantum gravity
• Spinor fields in Causal Set Theory

Cited by in corpus (9)

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• Ph.D. Thesis: Quantum Field Theory and Gravity in Causal Sets
• A note on discrete Holonomy through directed edges, with no lengths