Ultrarelativistic decoupling transformation for generalized Dirac equations

Noble, J. H. and Jentschura, Ulrich David (2015) Ultrarelativistic decoupling transformation for generalized Dirac equations. PHYSICAL REVIEW A, 92 (1). ISSN 2469-9926

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Abstract

The Foldy–Wouthuysen transformation is known to uncover the nonrelativistic limit of a gen- eralized Dirac Hamiltonian, lending an intuitive physical interpretation to the effective operators within Schr¨odinger–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 equa- tion 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.

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