3,837 research outputs found
Remarks on the structure constants of the Verlinde algebra associated to
The structure constants of the Verlinde
algebra as functions of either vanish or can be expressed after a change
of variable as the weight function of an irreducible representation of .
We give a similar formula in the case.Comment: 5 pages, AmsTeX, 1 figure available on reques
Alpha cluster condensation in 12C and 16O
A new -cluster wave function is proposed which is of the
-particle condensate type. Applications to C and O show
that states of low density close to the 3 resp. 4 -particle threshold
in both nuclei are possibly of this kind. It is conjectured that all
self-conjugate 4 nuclei may show similar features.Comment: 4 pages, 2 tables, 2 figure
Bound-State Variational Wave Equation For Fermion Systems In QED
We present a formulation of the Hamiltonian variational method for QED which
enables the derivation of relativistic few-fermion wave equation that can
account, at least in principle, for interactions to any order of the coupling
constant. We derive a relativistic two-fermion wave equation using this
approach. The interaction kernel of the equation is shown to be the generalized
invariant M-matrix including all orders of Feynman diagrams. The result is
obtained rigorously from the underlying QFT for arbitrary mass ratio of the two
fermions. Our approach is based on three key points: a reformulation of QED,
the variational method, and adiabatic hypothesis. As an application we
calculate the one-loop contribution of radiative corrections to the two-fermion
binding energy for singlet states with arbitrary principal quantum number ,
and . Our calculations are carried out in the explicitly covariant
Feynman gauge.Comment: 26 page
A reduced subduction graph and higher multiplicity in S_n transformation coefficients
Transformation coefficients between {\it standard} bases for irreducible
representations of the symmetric group and {\it split} bases adapted to
the subgroup () are
considered. We first provide a \emph{selection rule} and an \emph{identity
rule} for the subduction coefficients which allow to decrease the number of
unknowns and equations arising from the linear method by Pan and Chen. Then,
using the {\it reduced subduction graph} approach, we may look at higher
multiplicity instances. As a significant example, an orthonormalized solution
for the first multiplicity-three case, which occurs in the decomposition of the
irreducible representation of into
of , is presented and discussed.Comment: 12 pages, 1 figure, iopart class, Revisited version (several
typographical errors have been corrected). Accepted for publication in J.
Phys. A: Math. Ge
Matrix Models, Monopoles and Modified Moduli
Motivated by the Dijkgraaf-Vafa correspondence, we consider the matrix model
duals of N=1 supersymmetric SU(Nc) gauge theories with Nf flavors. We
demonstrate via the matrix model solutions a relation between vacua of theories
with different numbers of colors and flavors. This relation is due to an N=2
nonrenormalization theorem which is inherited by these N=1 theories.
Specializing to the case Nf=Nc, the simplest theory containing baryons, we
demonstrate that the explicit matrix model predictions for the locations on the
Coulomb branch at which monopoles condense are consistent with the quantum
modified constraints on the moduli in the theory. The matrix model solutions
include the case that baryons obtain vacuum expectation values. In specific
cases we check explicitly that these results are also consistent with the
factorization of corresponding Seiberg-Witten curves. Certain results are
easily understood in terms of M5-brane constructions of these gauge theories.Comment: 27 pages, LaTeX, 2 figure
Cube law, condition factor and weight-length relationships: history, meta-analysis and recommendations
This study presents a historical review, a meta-analysis, and recommendations for users about weight–length relationships, condition factors and relative weight equations. The historical review traces the developments of the respective concepts. The meta-analysis explores 3929 weight–length relationships of the type W = aLb for 1773 species of fishes. It shows that 82% of the variance in a plot of log a over b can be explained by allometric versus isometric growth patterns and by different body shapes of the respective species. Across species median b = 3.03 is significantly larger than 3.0, thus indicating a tendency towards slightly positive-allometric growth (increase in relative body thickness or plumpness) in most fishes. The expected range of 2.5 < b < 3.5 is confirmed. Mean estimates of b outside this range are often based on only one or two weight–length relationships per species. However, true cases of strong allometric growth do exist and three examples are given. Within species, a plot of log a vs b can be used to detect outliers in weight–length relationships. An equation to calculate mean condition factors from weight–length relationships is given as Kmean = 100aLb−3. Relative weight Wrm = 100W/(amLbm) can be used for comparing the condition of individuals across populations, where am is the geometric mean of a and bm is the mean of b across all available weight–length relationships for a given species. Twelve recommendations for proper use and presentation of weight–length relationships, condition factors and relative weight are given
Lie group weight multiplicities from conformal field theory
Dominant weight multiplicities of simple Lie groups are expressed in terms of
the modular matrices of Wess-Zumino-Witten conformal field theories, and
related objects. Symmetries of the modular matrices give rise to new relations
among multiplicities. At least for some Lie groups, these new relations are
strong enough to completely fix all multiplicities.Comment: 12 pages, Plain TeX, no figure
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