The Foldy-Wouthuysen transformation is known to uncover the nonrelativistic limit of a generalized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schrö dinger-Pauli 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 high-energy tachyons, which are faster-than-light particles described by a fully Lorentz-covariant equation. The effective gravitational interactions are found. For tachyons, the dominant gravitational interaction term in the high-energy limit is shown to be attractive and equal to the leading term for subluminal Dirac particles (tardyons) in the high-energy limit.
J. H. Noble and U. D. Jentschura, "Ultrarelativistic Decoupling Transformation for Generalized Dirac Equations," Physical Review A - Atomic, Molecular, and Optical Physics, vol. 92, no. 1, pp. 012101-1-012101-9, American Physical Society (APS), Jul 2015.
The definitive version is available at https://doi.org/10.1103/PhysRevA.92.012101
Keywords and Phrases
Covariant Equations; Decoupling Transformation; Effective Operator; Foldy-Wouthuysen Transformations; Generalized Dirac Equations; Gravitational Interaction; Nonrelativistic Limits; Physical Interpretation; Linear Equations
International Standard Serial Number (ISSN)
Article - Journal
© 2015 American Physical Society (APS), All rights reserved.
01 Jul 2015