Ultrarelativistic decoupling transformation for generalized Dirac equations
Abstract
The FoldyWouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within SchrödingerPauli theory. We here discuss the opposite, ultrarelativistic limit which requires the use of a fundamentally different expansion where the leading kinetic term in the Dirac equation is perturbed by the mass of the particle and other interaction (potential) terms, rather than vice versa. The ultrarelativistic decoupling transformation is applied to free Dirac particles (in the Weyl basis) and to highenergy tachyons, which are fasterthanlight particles described by a fully Lorentzcovariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the highenergy limit is shown to be attractive and equal to the leading term for subluminal Dirac particles (tardyons) in the highenergy limit.
 Publication:

Physical Review A
 Pub Date:
 July 2015
 DOI:
 10.1103/PhysRevA.92.012101
 arXiv:
 arXiv:1506.02504
 Bibcode:
 2015PhRvA..92a2101N
 Keywords:

 03.65.Pm;
 11.10.z;
 04.25.dg;
 95.36.+x;
 Relativistic wave equations;
 Field theory;
 Numerical studies of black holes and blackhole binaries;
 Dark energy;
 General Relativity and Quantum Cosmology;
 High Energy Physics  Phenomenology
 EPrint:
 10 pages