91 research outputs found
Aspects of Diffeomorphism Invariant Theory of Extended Objects
The structure of a diffeomorphism invariant Lagrangians for an extended
object W embedded in a bulk space M is discussed by following a close analogy
with the relativistic particle in electromagnetic field as a system that is
reparametrization-invariant. The current construction naturally contains,
relativistic point particle, string theory, and Dirac--Nambu--Goto Lagrangians
with Wess--Zumino terms. For Lorentzian metric field, the non-relativistic
theory of an integrally submerged W-brane is well defined provided that the
brane does not alter the background interaction fields. A natural time gauge is
fixed by the integral submergence (sub-manifold structure) within a Lorentzian
signature structure. A generally covariant relativistic theory for the
discussed brane Lagrangians is also discussed. The mass-shell constraint and
the Klein--Gordon equation are shown to be universal when gravity-like
interaction is present. A construction of the Dirac equation for the W-brane
that circumvents some of the problems associated with diffeomorphism invariance
of such Lagrangians by promoting the velocity coordinates into a non-commuting
gamma variables is presented.Comment: added references and minor format changes, 5 pages revtex4 style, no
figures, talk presented at the 3rd International Symposium on Quantum Theory
and Symmetries, and the Argonne Brane Dynamics Worksho
The Oblique Basis Method from an Engineering Point of View
The oblique basis method is reviewed from engineering point of view related
to vibration and control theory. Examples are used to demonstrate and relate
the oblique basis in nuclear physics to the equivalent mathematical problems in
vibration theory. The mathematical techniques, such as principal coordinates
and root locus, used by vibration and control theory engineers are shown to be
relevant to the Richardson - Gaudin pairing-like problems in nuclear physics.Comment: 7 pages, no figures, conference contribution to the Horizons of
Innovative Theories, Experiments, and Supercomputing in Nuclear Physics
http://www.phys.lsu.edu/hites2012
Mixed-Mode Shell-Model Calculations
A one-dimensional harmonic oscillator in a box is used to introduce the
oblique-basis concept. The method is extended to the nuclear shell model by
combining traditional spherical states, which yield a diagonal representation
of the usual single-particle interaction, with collective configurations that
track deformation. An application to 24Mg, using the realistic two-body
interaction of Wildenthal, is used to explore the validity of this mixed-mode
shell-model scheme. Specifically, the correct binding energy (within 2% of the
full-space result) as well as low-energy configurations that have greater than
90% overlap with full-space results are obtained in a space that spans less
than 10% of the full-space. The theory is also applied to lower pf-shell
nuclei, 44Ti-48Ti and 48Cr, using the Kuo-Brown-3 interaction. These nuclei
show strong SU(3) symmetry breaking due mainly to the single-particle
spin-orbit splitting. Nevertheless, the results also show that yrast band B(E2)
values are insensitive to fragmentation of the SU(3) symmetry. Specifically,
the quadrupole collectivity as measured by B(E2) strengths remains high even
though the SU(3) symmetry is rather badly broken. The IBM and broken-pair
models are considered as alternative basis sets for future oblique-basis
shell-model calculations.Comment: 3 pages, no figures, summary of a poster present at the Nuclear
Structure Conference: Mapping the Triangle. Grand Teton National Park,
Wyoming USA, May 22-25, 200
- …