eprintid: 1421894
rev_number: 41
eprint_status: archive
userid: 608
dir: disk0/01/42/18/94
datestamp: 2014-03-21 21:54:01
lastmod: 2021-10-04 01:39:46
status_changed: 2014-03-21 21:54:01
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Fang, Y-L
creators_name: Vassiliev, D
title: Analysis as a source of geometry: a non-geometric representation of the Dirac equation
ispublished: pub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
keywords: analysis of partial differential equations, gauge theory, Dirac equation
note: © 2015 IOP Publishing Ltd Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
abstract: Consider a formally self-adjoint first order linear differential operator acting on pairs (two-columns) of complex-valued scalar fields over a four-manifold without boundary. We examine the geometric content of such an operator and show that it implicitly contains a Lorentzian metric, Pauli matrices, connection coefficients for spinor fields and an electromagnetic covector potential. This observation allows us to give a simple representation of the massive Dirac equation as a system of four scalar equations involving an arbitrary two-by-two matrix operator as above and its adjugate. The point of the paper is that in order to write down the Dirac equation in the physically meaningful four-dimensional hyperbolic setting one does not need any geometric constructs. All the geometry required is contained in a single analytic object—an abstract formally self-adjoint first order linear differential operator acting on pairs of complex-valued scalar fields.
date: 2015-04-24
official_url: http://dx.doi.org/10.1088/1751-8113/48/16/165203
vfaculties: VMPS
oa_status: green
full_text_type: pub
primo: open
primo_central: open_green
verified: verified_manual
elements_source: WoS-Lite
elements_id: 923833
doi: 10.1088/1751-8113/48/16/165203
lyricists_name: Fang, Yanlong
lyricists_name: Vassiliev, Dmitri
lyricists_id: YLFAN45
lyricists_id: DVASS76
full_text_status: public
publication: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
volume: 48
number: 16
article_number: ARTN 165203
issn: 1751-8113
citation:        Fang, Y-L;    Vassiliev, D;      (2015)    Analysis as a source of geometry: a non-geometric representation of the Dirac equation.                   JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL , 48  (16)    , Article ARTN 165203.  10.1088/1751-8113/48/16/165203 <https://doi.org/10.1088/1751-8113%2F48%2F16%2F165203>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1421894/1/1751-8121_48_16_165203.pdf