20,497 research outputs found
Approximate Killing Vectors on S^2
We present a new method for computing the best approximation to a Killing
vector on closed 2-surfaces that are topologically S^2. When solutions of
Killing's equation do not exist, this method is shown to yield results superior
to those produced by existing methods. In addition, this method appears to
provide a new tool for studying the horizon geometry of distorted black holes.Comment: 4 pages, 3 figures, submitted to Physical Review D, revtex
A Classification of random Dirac fermions
We present a detailed classification of random Dirac hamiltonians in two
spatial dimensions based on the implementation of discrete symmetries. Our
classification is slightly finer than that of random matrices, and contains
thirteen classes. We also extend this classification to non-hermitian
hamiltonians with and without Dirac structure.Comment: 15 pages, version2: typos in the table of classes are correcte
Null-vectors in Integrable Field Theory
The form factor bootstrap approach allows to construct the space of local
fields in the massive restricted sine-Gordon model. This space has to be
isomorphic to that of the corresponding minimal model of conformal field
theory. We describe the subspaces which correspond to the Verma modules of
primary fields in terms of the commutative algebra of local integrals of motion
and of a fermion (Neveu-Schwarz or Ramond depending on the particular primary
field). The description of null-vectors relies on the relation between form
factors and deformed hyper-elliptic integrals. The null-vectors correspond to
the deformed exact forms and to the deformed Riemann bilinear identity. In the
operator language, the null-vectors are created by the action of two operators
\CQ (linear in the fermion) and \CC (quadratic in the fermion). We show
that by factorizing out the null-vectors one gets the space of operators with
the correct character. In the classical limit, using the operators \CQ and
\CC we obtain a new, very compact, description of the KdV hierarchy. We also
discuss a beautiful relation with the method of Whitham.Comment: 36 pages, Late
Integrable Spin Chain with Reflecting End
A new integrable spin chain of the Haldane-Shastry type is introduced. It is
interpreted as the inverse-square interacting spin chain with a {\it reflecting
end}. The lattice points of this model consist of the square roots of the zeros
of the Laguerre polynomial. Using the ``exchange operator formalism'', the
integrals of motion for the model are explicitly constructed.Comment: 13 pages, REVTeX3, with minor correction
Staggered Fermion Actions with Improved Rotational Invariance
We introduce a class of improved actions for staggered fermions which to
O(p^4) and O(p^6), respectively, lead to rotationally invariant propagators. We
discuss the resulting reduction of flavour symmetry breaking in the meson
spectrum and comment on the improvement in the calculation of thermodynamic
observables.Comment: 3 pages and 4 figures, Contribution to Lattice 97 (Poster Session),
late
On the Existence of Radiation Gauges in Petrov type II spacetimes
The radiation gauges used by Chrzanowski (his IRG/ORG) for metric
reconstruction in the Kerr spacetime seem to be over-specified. Their
specification consists of five conditions: four, which we treat here as valid
gauge conditions, plus an additional condition on the trace of the metric
perturbation. In this work, we utilize a newly developed form of the perturbed
Einstein equations to establish a condition -- on a particular tetrad component
of the stress-energy tensor -- under which the full IRG/ORG can be imposed.
Using gauge freedom, we are able to impose the full IRG for Petrov type II and
type D backgrounds, using a different tetrad for each case. As a specific
example, we work through the process of imposing the IRG in a Schwarzschild
background, using a more traditional approach. Implications for metric
reconstruction using the Teukolsky curvature perturbations in type D spacetimes
are briefly discussed.Comment: 21 pages, uses iop style files. v2: proved a stronger result for type
II backgrounds, added a subsection on remaining gauge freedom in the full IRG
and improved calrity and readability throughout due to insightful referee
comments; published as Class. Quantum Grav. 24 (2007) 2367-238
Thermodynamics of Lattice QCD with Chiral 4-Fermion Interactions
We have studied lattice QCD with an additional, irrelevant 4-fermion
interaction having a U(1)xU(1) chiral symmetry, at finite temperatures. Adding
this 4-fermion term allowed us to work at zero quark mass, which would have
otherwise been impossible. The theory with 2 massless staggered quark flavours
appears to have a first order finite temperature phase transition at N_t=4 for
the value of 4-fermion coupling we have chosen, in contrast to what is expected
for 2-flavour QCD. The pion screening mass is seen to vanish below this
transition, only to become massive and degenerate with the sigma (f_0) above
this transition where the chiral symmetry is restored, as is seen by the
vanishing of the chiral condensate.Comment: 23 pages, 11 figure
The Galactic dust as a foreground to Cosmic Microwave Background maps
We present results obtained with the PRONAOS balloon-borne experiment on
interstellar dust. In particular, the submillimeter / millimeter spectral index
is found to vary between roughly 1 and 2.5 on small scales (3.5' resolution).
This could have implications for component separation in Cosmic Microwave
Background maps.Comment: 4 pages, 1 figure, proceeding of the Multi-Wavelength Cosmology
conference held in Mykonos, Greece, June 2003, ed. Kluwe
Auxiliary field method and analytical solutions of the Schr\"{o}dinger equation with exponential potentials
The auxiliary field method is a new and efficient way to compute approximate
analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This
method has already been successfully applied to the case of central potentials
of power-law and logarithmic forms. In the present work, we show that the
Schr\"{o}dinger equation with exponential potentials of the form can also be analytically solved by using the
auxiliary field method. Formulae giving the critical heights and the energy
levels of these potentials are presented. Special attention is drawn on the
Yukawa potential and the pure exponential one
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