27 research outputs found
Spurious modes in extended RPA theories
Necessary conditions that the spurious state associated with the
translational motion and its double-phonon state have zero excitation energy in
extended RPA (ERPA) theories which include both one-body and two-body
amplitudes are investigated using the small amplitude limit of the
time-dependent density-matrix theory (STDDM). STDDM provides us with a quite
general form of ERPA as compared with other similar theories in the sense that
all components of one-body and two-body amplitudes are taken into account. Two
conditions are found necessary to guarantee the above property of the single
and double spurious states: The first is that no truncation in the
single-particle space should be made. This condition is necessary for the
closure relation to be used and is common for the single and double spurious
states. The second depends on the mode. For the single spurious state all
components of the one-body amplitudes must be included, and for the double
spurious state all components of one-body and two-body amplitudes have to be
included. It is also shown that the Kohn theorem and the continuity equations
for transition densities and currents hold under the same conditions as the
spurious states. ERPA theories formulated using the Hartree-Fock ground state
have a non-hermiticity problem. A method for formulating ERPA with hermiticity
is also proposed using the time-dependent density-matrix formalism.Comment: 15 page
Many worlds in one
A generic prediction of inflation is that the thermalized region we inhabit
is spatially infinite. Thus, it contains an infinite number of regions of the
same size as our observable universe, which we shall denote as \O-regions. We
argue that the number of possible histories which may take place inside of an
\O-region, from the time of recombination up to the present time, is finite.
Hence, there are an infinite number of \O-regions with identical histories up
to the present, but which need not be identical in the future. Moreover, all
histories which are not forbidden by conservation laws will occur in a finite
fraction of all \O-regions. The ensemble of \O-regions is reminiscent of
the ensemble of universes in the many-world picture of quantum mechanics. An
important difference, however, is that other \O-regions are unquestionably
real.Comment: 9 pages, 2 figures, comments and references adde
Neutrino masses: From fantasy to facts
Theory suggests the existence of neutrino masses, but little more. Facts are
coming close to reveal our fantasy: solar and atmospheric neutrino data
strongly indicate the need for neutrino conversions, while LSND provides an
intriguing hint. The simplest ways to reconcile these data in terms of neutrino
oscillations invoke a light sterile neutrino in addition to the three active
ones. Out of the four neutrinos, two are maximally-mixed and lie at the LSND
scale, while the others are at the solar mass scale. These schemes can be
distinguished at neutral-current-sensitive solar & atmospheric neutrino
experiments. I discuss the simplest theoretical scenarios, where the lightness
of the sterile neutrino, the nearly maximal atmospheric neutrino mixing, and
the generation of & all follow
naturally from the assumed lepton-number symmetry and its breaking. Although
the most likely interpretation of the present data is in terms of
neutrino-mass-induced oscillations, one still has room for alternative
explanations, such as flavour changing neutrino interactions, with no need for
neutrino mass or mixing. Such flavour violating transitions arise in theories
with strictly massless neutrinos, and may lead to other sizeable flavour
non-conservation effects, such as , conversion in
nuclei, unaccompanied by neutrino-less double beta decay.Comment: 33 pages, latex, 16 figures. Invited Talk at Ioannina Conference,
Symmetries in Intermediate High Energy Physics and its Applications, Oct.
1998, to be published by Springer Tracts in Modern Physics. Festschrift in
Honour of John Vergados' 60th Birthda