eprintid: 1424054
rev_number: 27
eprint_status: archive
userid: 608
dir: disk0/01/42/40/54
datestamp: 2014-03-22 19:48:04
lastmod: 2021-10-04 01:39:39
status_changed: 2014-03-22 19:48:04
type: article
metadata_visibility: show
item_issues_count: 0
creators_name: Fang, YL
creators_name: Vassiliev, D
title: Analysis of first order systems of partial differential equations
ispublished: unpub
divisions: UCL
divisions: B04
divisions: C06
divisions: F59
note: arXiv admin note: text overlap with arXiv:1401.3160
abstract: The paper deals with a formally self-adjoint first order linear differential operator acting on m-columns of complex-valued half-densities over an n-manifold without boundary. We study the distribution of eigenvalues in the elliptic setting and the propagator in the hyperbolic setting, deriving two-term asymptotic formulae for both. We then turn our attention to the special case of a two by two operator in dimension four. We show that the geometric concepts of Lorentzian metric, Pauli matrices, spinor field, connection coefficients for spinor fields, electromagnetic covector potential, Dirac equation and Dirac action arise naturally in the process of our analysis.
date: 2014-03-11
official_url: http://arxiv.org/abs/1403.2663
vfaculties: VMPS
oa_status: green
full_text_type: other
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_source: arXiv
elements_id: 937966
lyricists_name: Vassiliev, Dmitri
lyricists_id: DVASS76
full_text_status: public
citation:        Fang, YL;    Vassiliev, D;      (2014)    Analysis of first order systems of partial differential equations.                              Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/1424054/1/1403.2663v2.pdf