TY - JOUR

T1 - Semi-relativistic approximations of the Dirac equation : First and second order corrections

AU - Mauser, Norbert

N1 - Affiliations: Courant Institute, 251 Mercer Street, New York, NY 10012-1185, United States; Inst. F. Mathematik, Univ. Wien, Strudlhofg. 4, A - 1090 Wien, Austria
Adressen: Mauser, N.J.; Courant Institute; 251 Mercer Street New York, NY 10012-1185, United States; email: [email protected]
Source-File: 506Scopus.csv
Import aus Scopus: 2-s2.0-0034386084
Importdatum: 24.01.2007 11:28:13
22.10.2007: Datenanforderung 1920 (Import Sachbearbeiter)
04.01.2008: Datenanforderung 2054 (Import Sachbearbeiter)

PY - 2000

Y1 - 2000

N2 - We deal with the Dirac equation with time-dependent, non-homogeneous electro-magnetic potential, in particular with its approximation in the limit of infinite speed of light. For the linear case (given potential) we present a rigorous derivation of approximations in first and second order in the small parameter e = 1/c. Our method is based on the use of appropriate projection operators for the electron and the positron component of the spinor which are better suited than the simple splitting into "upper (large)" and "lower (small) component". We also discuss the question of a self-consistent modeling of the Pauli equation as the O(e) approximation. We suggest a coupling to an equation which is an "electro-magneto-static" O(e) approximation of the Maxwell equations consisting of Poisson equations for the four components of the potential.

AB - We deal with the Dirac equation with time-dependent, non-homogeneous electro-magnetic potential, in particular with its approximation in the limit of infinite speed of light. For the linear case (given potential) we present a rigorous derivation of approximations in first and second order in the small parameter e = 1/c. Our method is based on the use of appropriate projection operators for the electron and the positron component of the spinor which are better suited than the simple splitting into "upper (large)" and "lower (small) component". We also discuss the question of a self-consistent modeling of the Pauli equation as the O(e) approximation. We suggest a coupling to an equation which is an "electro-magneto-static" O(e) approximation of the Maxwell equations consisting of Poisson equations for the four components of the potential.

M3 - Article

VL - 29

SP - 449

EP - 464

JO - Transport Theory and Statistical Physics

JF - Transport Theory and Statistical Physics

SN - 0041-1450

IS - 3-5

ER -