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