Fang, YL;
Vassiliev, D;
(2014)
Analysis of first order systems of partial differential equations.
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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.
| Type: | Article |
|---|---|
| Title: | Analysis of first order systems of partial differential equations |
| Open access status: | An open access version is available from UCL Discovery |
| Publisher version: | http://arxiv.org/abs/1403.2663 |
| Language: | English |
| Additional information: | arXiv admin note: text overlap with arXiv:1401.3160 |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/1424054 |
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