1,345 research outputs found
Masses and Internal Structure of Mesons in the String Quark Model
The relativistic quantum string quark model, proposed earlier, is applied to
all mesons, from pion to , lying on the leading Regge trajectories
(i.e., to the lowest radial excitations in terms of the potential quark
models). The model describes the meson mass spectrum, and comparison with
measured meson masses allows one to determine the parameters of the model:
current quark masses, universal string tension, and phenomenological constants
describing nonstring short-range interaction. The meson Regge trajectories are
in general nonlinear; practically linear are only trajectories for light-quark
mesons with non-zero lowest spins. The model predicts masses of many new
higher-spin mesons. A new meson is predicted with mass 1910 Mev. In
some cases the masses of new low-spin mesons are predicted by extrapolation of
the phenomenological short-range parameters in the quark masses. In this way
the model predicts the mass of to be MeV, and
the mass of to be MeV (the potential model predictions
are 100 Mev lower). The relativistic wave functions of the composite mesons
allow one to calculate the energy and spin structure of mesons. The average
quark-spin projections in polarized -meson are twice as small as the
nonrelativistic quark model predictions. The spin structure of reveals an
80% violation of the flavour SU(3). These results may be relevant to
understanding the ``spin crises'' for nucleons.Comment: 30 pages, REVTEX, 6 table
Free Boundary Poisson Bracket Algebra in Ashtekar's Formalism
We consider the algebra of spatial diffeomorphisms and gauge transformations
in the canonical formalism of General Relativity in the Ashtekar and ADM
variables. Modifying the Poisson bracket by including surface terms in
accordance with our previous proposal allows us to consider all local
functionals as differentiable. We show that closure of the algebra under
consideration can be achieved by choosing surface terms in the expressions for
the generators prior to imposing any boundary conditions. An essential point is
that the Poisson structure in the Ashtekar formalism differs from the canonical
one by boundary terms.Comment: 19 pages, Latex, amsfonts.sty, amssymb.st
Putting an Edge to the Poisson Bracket
We consider a general formalism for treating a Hamiltonian (canonical) field
theory with a spatial boundary. In this formalism essentially all functionals
are differentiable from the very beginning and hence no improvement terms are
needed. We introduce a new Poisson bracket which differs from the usual
``bulk'' Poisson bracket with a boundary term and show that the Jacobi identity
is satisfied. The result is geometrized on an abstract world volume manifold.
The method is suitable for studying systems with a spatial edge like the ones
often considered in Chern-Simons theory and General Relativity. Finally, we
discuss how the boundary terms may be related to the time ordering when
quantizing.Comment: 36 pages, LaTeX. v2: A manifest formulation of the Poisson bracket
and some examples are added, corrected a claim in Appendix C, added an
Appendix F and a reference. v3: Some comments and references adde
Twisted convolution and Moyal star product of generalized functions
We consider nuclear function spaces on which the Weyl-Heisenberg group acts
continuously and study the basic properties of the twisted convolution product
of the functions with the dual space elements. The final theorem characterizes
the corresponding algebra of convolution multipliers and shows that it contains
all sufficiently rapidly decreasing functionals in the dual space.
Consequently, we obtain a general description of the Moyal multiplier algebra
of the Fourier-transformed space. The results extend the Weyl symbol calculus
beyond the traditional framework of tempered distributions.Comment: LaTeX, 16 pages, no figure
Asymptotic Infrared Fractal Structure of the Propagator for a Charged Fermion
It is well known that the long-range nature of the Coulomb interaction makes
the definition of asymptotic ``in'' and ``out'' states of charged particles
problematic in quantum field theory. In particular, the notion of a simple
particle pole in the vacuum charged particle propagator is untenable and should
be replaced by a more complicated branch cut structure describing an electron
interacting with a possibly infinite number of soft photons. Previous work
suggests a Dirac propagator raised to a fractional power dependent upon the
fine structure constant, however the exponent has not been calculated in a
unique gauge invariant manner. It has even been suggested that the fractal
``anomalous dimension'' can be removed by a gauge transformation. Here, a gauge
invariant non-perturbative calculation will be discussed yielding an
unambiguous fractional exponent. The closely analogous case of soft graviton
exponents is also briefly explored.Comment: Updated with a corrected sign error, longer discussion of fractal
dimension, and more reference
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