An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid

Martin Sikora

Archivum Mathematicum (2010)

  • Volume: 046, Issue: 5, page 363-376
  • ISSN: 0044-8753

Abstract

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The Dirac equation for spinor-valued fields f on the Minkowski space of even dimension form a hyperbolic system of partial differential equations. In the paper, we are showing how to reconstruct the solution from initial data given on the upper sheet H + of the hyperboloid. In particular, we derive an integral formula expressing the value of f in a chosen point p as an integral over a compact cycle given by the intersection of the null cone with H + in the Minkowski space 𝕄 .

How to cite

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Sikora, Martin. "An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid." Archivum Mathematicum 046.5 (2010): 363-376. <http://eudml.org/doc/116499>.

@article{Sikora2010,
abstract = {The Dirac equation for spinor-valued fields $f$ on the Minkowski space of even dimension form a hyperbolic system of partial differential equations. In the paper, we are showing how to reconstruct the solution from initial data given on the upper sheet $H^+$ of the hyperboloid. In particular, we derive an integral formula expressing the value of $f$ in a chosen point $p$ as an integral over a compact cycle given by the intersection of the null cone with $H^+$ in the Minkowski space $\{\mathbb \{M\}\}$.},
author = {Sikora, Martin},
journal = {Archivum Mathematicum},
keywords = {Clifford analysis; integral formula of hyperbolic type; hyperboloid; Minkowski space; Clifford analysis; integral formula of hyperbolic type; hyperboloid; Minkowski space},
language = {eng},
number = {5},
pages = {363-376},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid},
url = {http://eudml.org/doc/116499},
volume = {046},
year = {2010},
}

TY - JOUR
AU - Sikora, Martin
TI - An integral formula of hyperbolic type for solutions of the Dirac equation on Minkowski space with initial conditions on a hyperboloid
JO - Archivum Mathematicum
PY - 2010
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 046
IS - 5
SP - 363
EP - 376
AB - The Dirac equation for spinor-valued fields $f$ on the Minkowski space of even dimension form a hyperbolic system of partial differential equations. In the paper, we are showing how to reconstruct the solution from initial data given on the upper sheet $H^+$ of the hyperboloid. In particular, we derive an integral formula expressing the value of $f$ in a chosen point $p$ as an integral over a compact cycle given by the intersection of the null cone with $H^+$ in the Minkowski space ${\mathbb {M}}$.
LA - eng
KW - Clifford analysis; integral formula of hyperbolic type; hyperboloid; Minkowski space; Clifford analysis; integral formula of hyperbolic type; hyperboloid; Minkowski space
UR - http://eudml.org/doc/116499
ER -

References

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