17,651 research outputs found
Convergent series for lattice models with polynomial interactions
The standard perturbative weak-coupling expansions in lattice models are
asymptotic. The reason for this is hidden in the incorrect interchange of the
summation and integration. However, substituting the Gaussian initial
approximation of the perturbative expansions by a certain interacting model or
regularizing original lattice integrals, one can construct desired convergent
series. In this paper we develop methods, which are based on the joint and
separate utilization of the regularization and new initial approximation. We
prove, that the convergent series exist and can be expressed as the re-summed
standard perturbation theory for any model on the finite lattice with the
polynomial interaction of even degree. We discuss properties of such series and
make them applicable to practical computations. The workability of the methods
is demonstrated on the example of the lattice -model. We calculate the
operator using the convergent series, the comparison
of the results with the Borel re-summation and Monte Carlo simulations shows a
good agreement between all these methods.Comment: 25 pages, 14 figure
A Mathematica Package for Computing N=2 Superfield Operator Product Expansions
We describe a general purpose Mathematica package for computing Superfield
Operator Product Expansions in meromorphic superconformal field theory.
Given the SOPEs for a set of ``basic" superfields, SOPEs of arbitrarily
complicated composites can be computed automatically. Normal ordered products
are always reduced to a standard form. It is possible to check the Jacobi
identities, and to compute Poisson brackets (``classical SOPEs''). We present
two explicit examples: a construction of the ``small'' superconformal
algebra in terms of superfields, and a realisation of the
superconformal algebra in terms of chiral and antichiral fermionic superfields.Comment: 15 pages, LaTeX. Minor corrections, particularly to Mathematica
output Out[6],Out[9] in section 4. Available through anonymous ftp from
ftp://euclid.tp.ph.ic.ac.uk/papers/ or on WWW at
http://euclid.tp.ph.ic.ac.uk/Papers
Solution of the Riemann problem for polarization waves in a two-component Bose-Einstein condensate
We provide a classification of the possible flow of two-component
Bose-Einstein condensates evolving from initially discontinuous profiles. We
consider the situation where the dynamics can be reduced to the consideration
of a single polarization mode (also denoted as "magnetic excitation") obeying a
system of equations equivalent to the Landau-Lifshitz equation for an
easy-plane ferro-magnet. We present the full set of one-phase periodic
solutions. The corresponding Whitham modulation equations are obtained together
with formulas connecting their solutions with the Riemann invariants of the
modulation equations. The problem is not genuinely nonlinear, and this results
in a non-single-valued mapping of the solutions of the Whitham equations with
physical wave patterns as well as to the appearance of new elements --- contact
dispersive shock waves --- that are absent in more standard, genuinely
nonlinear situations. Our analytic results are confirmed by numerical
simulations
Charged analogue of Finch-Skea stars
We present solutions to the Einstein-Maxwell system of equations in
spherically symmetric gravitational fields for static interior spacetimes with
a specified form of the electric field intensity. The condition of pressure
isotropy yields three category of solutions. The first category is expressible
in terms of elementary functions and does not have an uncharged limit. The
second category is given in terms of Bessel functions of half-integer order.
These charged solutions satisfy a barotropic equation of state and contain
Finch-Skea uncharged stars. The third category is obtained in terms of modified
Bessel functions of half-integer order and does not have an uncharged limit.
The physical features of the charged analogue of the Finch-Skea stars are
studied in detail. In particular the condition of causality is satisfied and
the speed of sound does not exceed the speed of light. The physical analysis
indicates that this analogue is a realistic model for static charged
relativistic perfect fluid spheres.Comment: 17 pages, To appear in Int. J. Mod. Phys.
Nonlinear Realization and Weyl Scale Invariant p=2 Brane
The action of Weyl scale invariant p=2 brane which breaks the target super
Weyl scale symmetry in the N=1, D=4 superspace down to the lower dimensional
Weyl symmetry W(1,2) is derived by the approach of nonlinear realization. The
dual form action for the Weyl scale invariant supersymmetric D2 brane is also
constructed. The interactions of localized matter fields on the brane with the
Nambu-Goldstone fields associated with the breaking of the symmetries in the
superspace and one spatial translation directions are obtained through the
Cartan one-forms of the Coset structures. The covariant derivatives for the
localized matter fields are also obtained by introducing Weyl gauge field as
the compensating field corresponding to the local scale transformation on the
brane world volume.Comment: 20 page
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