### Abstract

We deal with consistent first order non-relativistic corrections (i.e. in the small parameter ε = 1/c, where c is the speed of light) of the Dirac-Maxwell system. We discuss a selfconsistent modeling of the Pauli equation as the O(ε) approximation of the Dirac equation. We suggest a coupling to the "magnetostatic" O(ε) approximation of the Maxwell equations consisting of Poisson equations for the four components of the potential. We sketch the semiclassical/nonrelativistic limits of this model.

Original language | English (US) |
---|---|

Pages (from-to) | 19-24 |

Number of pages | 6 |

Journal | Monatshefte fur Mathematik |

Volume | 132 |

Issue number | 1 |

DOIs | |

State | Published - 2001 |

### Fingerprint

### Keywords

- Dirac equation
- Maxwell equation
- Nonlinear PDE
- Nonrelativistic limit
- Poisson equation

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Monatshefte fur Mathematik*,

*132*(1), 19-24. https://doi.org/10.1007/s006050170055

**The selfconsistent Pauli equation.** / Masmoudi, Nader; Mauser, Norbert J.

Research output: Contribution to journal › Article

*Monatshefte fur Mathematik*, vol. 132, no. 1, pp. 19-24. https://doi.org/10.1007/s006050170055

}

TY - JOUR

T1 - The selfconsistent Pauli equation

AU - Masmoudi, Nader

AU - Mauser, Norbert J.

PY - 2001

Y1 - 2001

N2 - We deal with consistent first order non-relativistic corrections (i.e. in the small parameter ε = 1/c, where c is the speed of light) of the Dirac-Maxwell system. We discuss a selfconsistent modeling of the Pauli equation as the O(ε) approximation of the Dirac equation. We suggest a coupling to the "magnetostatic" O(ε) approximation of the Maxwell equations consisting of Poisson equations for the four components of the potential. We sketch the semiclassical/nonrelativistic limits of this model.

AB - We deal with consistent first order non-relativistic corrections (i.e. in the small parameter ε = 1/c, where c is the speed of light) of the Dirac-Maxwell system. We discuss a selfconsistent modeling of the Pauli equation as the O(ε) approximation of the Dirac equation. We suggest a coupling to the "magnetostatic" O(ε) approximation of the Maxwell equations consisting of Poisson equations for the four components of the potential. We sketch the semiclassical/nonrelativistic limits of this model.

KW - Dirac equation

KW - Maxwell equation

KW - Nonlinear PDE

KW - Nonrelativistic limit

KW - Poisson equation

UR - http://www.scopus.com/inward/record.url?scp=0035664744&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035664744&partnerID=8YFLogxK

U2 - 10.1007/s006050170055

DO - 10.1007/s006050170055

M3 - Article

AN - SCOPUS:0035664744

VL - 132

SP - 19

EP - 24

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 1

ER -