Berlin 2005 – wissenschaftliches Programm
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GR: Gravitation und Relativitätstheorie
GR 3: Supersymmetrie, SYM
GR 3.3: Vortrag
Freitag, 4. März 2005, 12:15–12:30, TU BH262
Supersymmetry, exact Foldy-Wouthuysen transformation and gravity — •Sebastian Heidenreich, Thoralf Chrobok, and Horst-Heino v. Borzeszkowski — Institut für Theoretische Physik PN7-1, TU Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
The Dirac particle in general space-time metrics is considered and
the Dirac Hamiltonian in Newman-Penrose formalism is constructed. To
get the physical meaning of the Dirac Hamiltonian it is necessary to
perform the Foldy-Wouthuysen transformation. In most cases this
transformation exists only in approximative form. Here we show that
for supersymmetric Dirac Hamiltonians depending not explicitly on
time the exact Foldy-Wouthuysen transformation can always be
constructed.
Further we give some criterions for spin coefficients such that the accompanying Dirac Hamiltonian is supersymmetric. These criterions are
fulfilled by the class of static axisymmetric space-time metrics.
Recently Obukhov [1] constructed a different exact Foldy-Wouthuysen
transformation for the subclass of conform-stationary space-time
metrics and calculated the Dirac-Hamiltonian in Foldy-Wouthuysen
representation. We show that the expansion series in orders of
1/mc2 of our Dirac Hamiltonian and Obukhov’s one coincide.
[1] Y. N. Obukhov, Phys. Rev. Lett. 86, 2001, 192