8 research outputs found
Equivalent forms of Dirac equations in curved spacetimes and generalized de Broglie relations
One may ask whether the relations between energy and frequency and between
momentum and wave vector, introduced for matter waves by de Broglie, are
rigorously valid in the presence of gravity. In this paper, we show this to be
true for Dirac equations in a background of gravitational and electromagnetic
fields. We first transform any Dirac equation into an equivalent canonical
form, sometimes used in particular cases to solve Dirac equations in a curved
spacetime. This canonical form is needed to apply the Whitham Lagrangian
method. The latter method, unlike the WKB method, places no restriction on the
magnitude of Planck's constant to obtain wave packets, and furthermore
preserves the symmetries of the Dirac Lagrangian. We show using canonical Dirac
fields in a curved spacetime, that the probability current has a Gordon
decomposition into a convection current and a spin current, and that the spin
current vanishes in the Whitham approximation, which explains the negligible
effect of spin on wave packet solutions, independent of the size of Planck's
constant. We further discuss the classical-quantum correspondence in a curved
spacetime based on both Lagrangian and Hamiltonian formulations of the Whitham
equations. We show that the generalized de Broglie relations in a curved
spacetime are a direct consequence of Whitham's Lagrangian method, and not just
a physical hypothesis as introduced by Einstein and de Broglie, and by many
quantum mechanics textbooks.Comment: PDF, 32 pages in referee format. Added significant material on
canonical forms of Dirac equations. Simplified Theorem 1 for normal Dirac
equations. Added section on Gordon decomposition of the probability current.
Encapsulated main results in the statement of Theorem
Measurement of the spin structure of the deuteron in the DIS region
Ageev ES, Alexakhin VY, Alexandrov Y, et al. Measurement of the spin structure of the deuteron in the DIS region. Phys.Lett. B. 2005;612(3-4):154-164.We present a new measurement of the longitudinal spin asymmetry Ad and the spin-dependent structure function g(1)(d) of the deuteron in the range 1 < Q(2) < 100 GeV2 and 0.004 < x < 0.7. The data were obtained by the COMPASS experiment at CERN using a 160 GeV polarised muon beam and a large polarised (LiD)-Li-6 target. The results are in agreement with those from previous experiments and improve considerably the statistical accuracy in the region 0.004 < x < 0.03. (c) 2005 Elsevier B.V. All rights reserved