5 research outputs found
The physical meaning of the de Sitter invariants
We study the Lie algebras of the covariant representations transforming the
matter fields under the de Sitter isometries. We point out that the Casimir
operators of these representations can be written in closed forms and we deduce
how their eigenvalues depend on the field's rest energy and spin. For the
scalar, vector and Dirac fields, which have well-defined field equations, we
express these eigenvalues in terms of mass and spin obtaining thus the
principal invariants of the theory of free fields on the de Sitter spacetime.
We show that in the flat limit we recover the corresponding invariants of the
Wigner irreducible representations of the Poincare group.Comment: 22 pages no figure
Polarized Dirac fermions in de Sitter spacetime
The tetrad gauge invariant theory of the free Dirac field in two special
moving charts of the de Sitter spacetime is investigated pointing out the
operators that commute with the Dirac one. These are the generators of the
symmetry transformations corresponding to isometries that give rise to
conserved quantities according to the Noether theorem. With their help the
plane wave spinor solutions of the Dirac equation with given momentum and
helicity are derived and the final form of the quantum Dirac field is
established. It is shown that the canonical quantization leads to a correct
physical interpretation of the massive or massless fermion quantum fields.Comment: 19 pages, LaTeX w AMS sym
The Dirac operator on generalized Taub-NUT spaces
We find sufficient conditions for the absence of harmonic spinors on
spin manifolds constructed as cone bundles over a compact K\"ahler base. These
conditions are fulfilled for certain perturbations of the Euclidean metric, and
also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a
conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page
The Dirac system on the Anti-de Sitter Universe
We investigate the global solutions of the Dirac equation on the
Anti-de-Sitter Universe. Since this space is not globally hyperbolic, the
Cauchy problem is not, {\it a priori}, well-posed. Nevertheless we can prove
that there exists unitary dynamics, but its uniqueness crucially depends on the
ratio beween the mass of the field and the cosmological constant
: it appears a critical value, , which plays a role
similar to the Breitenlohner-Freedman bound for the scalar fields. When
there exists a unique unitary dynamics. In opposite, for
the light fermions satisfying , we construct several asymptotic
conditions at infinity, such that the problem becomes well-posed. In all the
cases, the spectrum of the hamiltonian is discrete. We also prove a result of
equipartition of the energy.Comment: 33 page
Absorption and quasinormal modes of classical fields propagating on 3D and 4D de Sitter spacetime
We extensively study the exact solutions of the massless Dirac equation in 3D
de Sitter spacetime that we published recently. Using the Newman-Penrose
formalism, we find exact solutions of the equations of motion for the massless
classical fields of spin s=1/2,1,2 and to the massive Dirac equation in 4D de
Sitter metric. Employing these solutions, we analyze the absorption by the
cosmological horizon and de Sitter quasinormal modes. We also comment on the
results given by other authors.Comment: 31 page