Coupling Non-Gravitational Fields with Simplicial Spacetimes release_k2erhjihnrgjlgohrybeggaiie

by Jonathan R. McDonald, Warner A. Miller

Released as a article .

2010  

Abstract

The inclusion of source terms in discrete gravity is a long-standing problem. Providing a consistent coupling of source to the lattice in Regge Calculus (RC) yields a robust unstructured spacetime mesh applicable to both numerical relativity and quantum gravity. RC provides a particularly insightful approach to this problem with its purely geometric representation of spacetime. The simplicial building blocks of RC enable us to represent all matter and fields in a coordinate-free manner. We provide an interpretation of RC as a discrete exterior calculus framework into which non-gravitational fields naturally couple with the simplicial lattice. Using this approach we obtain a consistent mapping of the continuum action for non-gravitational fields to the Regge lattice. In this paper we apply this framework to scalar, vector and tensor fields. In particular we reconstruct the lattice action for (1) the scalar field, (2) Maxwell field tensor and (3) Dirac particles. The straightforward application of our discretization techniques to these three fields demonstrates a universal implementation of coupling source to the lattice in Regge calculus.
In text/plain format

Archived Files and Locations

application/pdf  167.3 kB
file_3jrfjsc3fvagrmvnfl6iumizxm
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2010-02-26
Version   v1
Language   en ?
arXiv  1002.5001v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 89fe7c9a-e333-41fe-8ca9-643a573fc719
API URL: JSON