3,121 research outputs found
Renormalization Group and Infinite Algebraic Structure in D-Dimensional Conformal Field Theory
We consider scalar field theory in the D-dimensional space with nontrivial
metric and local action functional of most general form. It is possible to
construct for this model a generalization of renormalization procedure and
RG-equations. In the fixed point the diffeomorphism and Weyl transformations
generate an infinite algebraic structure of D-Dimensional conformal field
theory models. The Wilson expansion and crossing symmetry enable to obtain sum
rules for dimensions of composite operators and Wilson coefficients.Comment: 16 page
Breakdown of scale-invariance in the coarsening of phase-separating binary fluids
We present evidence, based on lattice Boltzmann simulations, to show that the
coarsening of the domains in phase separating binary fluids is not a
scale-invariant process. Moreover we emphasise that the pathway by which phase
separation occurs depends strongly on the relation between diffusive and
hydrodynamic time scales.Comment: 4 pages, Latex, 4 eps Figures included. (higher quality Figures can
be obtained from [email protected]
AdS/CFT for Four-Point Amplitudes involving Gravitino Exchange
In this paper we compute the tree-level four-point scattering amplitude of
two dilatini and two axion-dilaton fields in type IIB supergravity in AdS5 x
S5. A special feature of this process is that there is an "exotic" channel in
which there are no singleparticle poles. Another novelty is that this process
involves the exchange of a bulk gravitino. The amplitude is interpreted in
terms of N = 4 supersymmetric Yang-Mills theory at large 't Hooft coupling.
Properties of the Operator Product Expansion are used to analyze the various
contributions from single- and double-trace operators in the weak and strongly
coupled regimes, and to determine the anomalous dimensions of semi-short
operators. The analysis is particularly clear in the exotic channel, given the
absence of BPS states.Comment: 32 pages, 1 figure. Published Version. Minor change
Random Matrices and the Convergence of Partition Function Zeros in Finite Density QCD
We apply the Glasgow method for lattice QCD at finite chemical potential to a
schematic random matrix model (RMM). In this method the zeros of the partition
function are obtained by averaging the coefficients of its expansion in powers
of the chemical potential. In this paper we investigate the phase structure by
means of Glasgow averaging and demonstrate that the method converges to the
correct analytically known result. We conclude that the statistics needed for
complete convergence grows exponentially with the size of the system, in our
case, the dimension of the Dirac matrix. The use of an unquenched ensemble at
does not give an improvement over a quenched ensemble.
We elucidate the phenomenon of a faster convergence of certain zeros of the
partition function. The imprecision affecting the coefficients of the
polynomial in the chemical potential can be interpeted as the appearance of a
spurious phase. This phase dominates in the regions where the exact partition
function is exponentially small, introducing additional phase boundaries, and
hiding part of the true ones. The zeros along the surviving parts of the true
boundaries remain unaffected.Comment: 17 pages, 14 figures, typos correcte
Quantum Mechanics as an Approximation to Classical Mechanics in Hilbert Space
Classical mechanics is formulated in complex Hilbert space with the
introduction of a commutative product of operators, an antisymmetric bracket,
and a quasidensity operator. These are analogues of the star product, the Moyal
bracket, and the Wigner function in the phase space formulation of quantum
mechanics. Classical mechanics can now be viewed as a deformation of quantum
mechanics. The forms of semiquantum approximations to classical mechanics are
indicated.Comment: 10 pages, Latex2e file, references added, minor clarifications mad
Twenty Years of the Weyl Anomaly
In 1973 two Salam prot\'{e}g\'{e}s (Derek Capper and the author) discovered
that the conformal invariance under Weyl rescalings of the metric tensor
displayed by classical
massless field systems in interaction with gravity no longer survives in the
quantum theory. Since then these Weyl anomalies have found a variety of
applications in black hole physics, cosmology, string theory and statistical
mechanics. We give a nostalgic review. (Talk given at the {\it Salamfest},
ICTP, Trieste, March 1993.)Comment: 43 page
Conformal Symmetry and the Three Point Function for the Gravitational Axial Anomaly
This work presents a first study of a radiative calculation for the
gravitational axial anomaly in the massless Abelian Higgs model. The two loop
contribution to the anomalous correlation function of one axial current and two
energy-momentum tensors, , is computed
at an order that involves only internal matter fields. Conformal properties of
massless field theories are used in order to perform the Feynman diagram
calculations in the coordinate space representation. The two loop contribution
is found not to vanish, due to the presence of two independent tensor
structures in the anomalous correlator.Comment: 34 pages, 5 figures, RevTex, Minor changes, Final version for Phys.
Rev.
Analytic Solution for the Critical State in Superconducting Elliptic Films
A thin superconductor platelet with elliptic shape in a perpendicular
magnetic field is considered. Using a method originally applied to circular
disks, we obtain an approximate analytic solution for the two-dimensional
critical state of this ellipse. In the limits of the circular disk and the long
strip this solution is exact, i.e. the current density is constant in the
region penetrated by flux. For ellipses with arbitrary axis ratio the obtained
current density is constant to typically 0.001, and the magnetic moment
deviates by less than 0.001 from the exact value. This analytic solution is
thus very accurate. In increasing applied magnetic field, the penetrating flux
fronts are approximately concentric ellipses whose axis ratio b/a < 1 decreases
and shrinks to zero when the flux front reaches the center, the long axis
staying finite in the fully penetrated state. Analytic expressions for these
axes, the sheet current, the magnetic moment, and the perpendicular magnetic
field are presented and discussed. This solution applies also to
superconductors with anisotropic critical current if the anisotropy has a
particular, rather realistic form.Comment: Revtex file and 13 postscript figures, gives 10 pages of text with
figures built i
Difference Operator Approach to the Moyal Quantization and Its Application to Integrable Systems
Inspired by the fact that the Moyal quantization is related with nonlocal
operation, I define a difference analogue of vector fields and rephrase quantum
description on the phase space. Applying this prescription to the theory of the
KP-hierarchy, I show that their integrability follows to the nature of their
Wigner distribution. Furthermore the definition of the ``expectation value''
clarifies the relation between our approach and the Hamiltonian structure of
the KP-hierarchy. A trial of the explicit construction of the Moyal bracket
structure in the integrable system is also made.Comment: 19 pages, to appear in J. Phys. Soc. Jp
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