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Full-Text Articles in Physical Sciences and Mathematics
Ultrarelativistic Decoupling Transformation For Generalized Dirac Equations, J. H. Noble, Ulrich D. Jentschura
Ultrarelativistic Decoupling Transformation For Generalized Dirac Equations, J. H. Noble, Ulrich D. Jentschura
Physics Faculty Research & Creative Works
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 …
Nonrelativistic Limit Of The Dirac-Schwarzschild Hamiltonian: Gravitational Zitterbewegung And Gravitational Spin-Orbit Coupling, Ulrich D. Jentschura, J. H. Noble
Nonrelativistic Limit Of The Dirac-Schwarzschild Hamiltonian: Gravitational Zitterbewegung And Gravitational Spin-Orbit Coupling, Ulrich D. Jentschura, J. H. Noble
Physics Faculty Research & Creative Works
We investigate the nonrelativistic limit of the gravitationally coupled Dirac equation via a Foldy-Wouthuysen transformation. The relativistic correction terms have immediate and obvious physical interpretations in terms of a gravitational Zitterbewegung and a gravitational spin-orbit coupling. We find no direct coupling of the spin vector to the gravitational force, which would otherwise violate parity. The particle-antiparticle symmetry described recently by one of us is verified on the level of the perturbative corrections accessed by the Foldy-Wouthuysen transformation. The gravitational corrections to the electromagnetic transition current are calculated.
Gravitationally Coupled Dirac Equation For Antimatter, Ulrich D. Jentschura
Gravitationally Coupled Dirac Equation For Antimatter, Ulrich D. Jentschura
Physics Faculty Research & Creative Works
The coupling of antimatter to gravity is of general interest because of conceivable cosmological consequences ("surprises") related to dark energy and the cosmological constant. Here, we revisit the derivation of the gravitationally coupled Dirac equation and find that the prefactor of a result given previously by Brill and Wheeler [Rev. Mod. Phys. 29, 465 (1957)] for the affine connection matrix is in need of a correction. We also discuss the conversion of the curved-space Dirac equation from the so-called "East-Coast" to the "West-Coast" convention, in order to bring the gravitationally coupled Dirac equation to a form where it can easily …
Self-Energy Correction To The Bound-Electron G Factor Of P States, Ulrich D. Jentschura
Self-Energy Correction To The Bound-Electron G Factor Of P States, Ulrich D. Jentschura
Physics Faculty Research & Creative Works
The radiative self-energy correction to the bound-electron g factor of 2P1/2 and 2P3/2 states in one-electron ions is evaluated to order α(Zα)2. The contribution of high-energy virtual photons is treated by means of an effective Dirac equation, and the result is verified by an approach based on long-wavelength quantum electrodynamics. The contribution of low-energy virtual photons is calculated both in the velocity and in the length gauge, and gauge invariance is verified explicitly. The results compare favorably to recently available numerical data for hydrogenlike systems with low nuclear charge numbers.