48 research outputs found
Analytical results for the confinement mechanism in QCD_3
We present analytical methods for investigating the interaction of two heavy
quarks in QCD_3 using the effective action approach. Our findings result in
explicit expressions for the static potentials in QCD_3 for long and short
distances. With regard to confinement, our conclusion reflects many features
found in the more realistic world of QCD_4.Comment: 24 pages, uses REVTe
Massive Spinning Particle in Any Dimension I. Integer Spins
The Kirillov-Souriau-Kostant construction is applied to derive the classical
and quantum mechanics for the massive spinning particle in arbitrary dimension.Comment: 13 pages, LaTe
Supersymmetric vertex algebras
We define and study the structure of SUSY Lie conformal and vertex algebras.
This leads to effective rules for computations with superfields.Comment: 71 page
Mean Field Fluid Behavior of the Gaussian Core Model
We show that the Gaussian core model of particles interacting via a
penetrable repulsive Gaussian potential, first considered by Stillinger (J.
Chem. Phys. 65, 3968 (1976)), behaves like a weakly correlated ``mean field
fluid'' over a surprisingly wide density and temperature range. In the bulk the
structure of the fluid phase is accurately described by the random phase
approximation for the direct correlation function, and by the more
sophisticated HNC integral equation. The resulting pressure deviates very
little from a simple, mean-field like, quadratic form in the density, while the
low density virial expansion turns out to have an extremely small radius of
convergence. Density profiles near a hard wall are also very accurately
described by the corresponding mean-field free-energy functional. The binary
version of the model exhibits a spinodal instability against de-mixing at high
densities. Possible implications for semi-dilute polymer solutions are
discussed.Comment: 13 pages, 2 columns, ReVTeX epsfig,multicol,amssym, 15 figures;
submitted to Phys. Rev. E (change: important reference added
Poisson sigma model on the sphere
We evaluate the path integral of the Poisson sigma model on sphere and study
the correlators of quantum observables. We argue that for the path integral to
be well-defined the corresponding
Poisson structure should be unimodular. The construction of the finite
dimensional BV theory is presented and we argue that it is responsible for the
leading semiclassical contribution. For a (twisted) generalized Kahler manifold
we discuss the gauge fixed action for the Poisson sigma model. Using the
localization we prove that for the holomorphic Poisson structure the
semiclassical result for the correlators is indeed the full quantum result.Comment: 38 page
Quantum phase transition in the Frenkel-Kontorova chain: from pinned instanton glass to sliding phonon gas
We study analytically and numerically the one-dimensional quantum
Frenkel-Kontorova chain in the regime when the classical model is located in
the pinned phase characterized by the gaped phonon excitations and devil's
staircase. By extensive quantum Monte Carlo simulations we show that for the
effective Planck constant smaller than the critical value the
quantum chain is in the pinned instanton glass phase. In this phase the
elementary excitations have two branches: phonons, separated from zero energy
by a finite gap, and instantons which have an exponentially small excitation
energy. At the quantum phase transition takes place and for
the pinned instanton glass is transformed into the sliding
phonon gas with gapless phonon excitations. This transition is accompanied by
the divergence of the spatial correlation length and appearence of sliding
modes at .Comment: revtex 16 pages, 18 figure
Generalized Drinfeld-Sokolov Reductions and KdV Type Hierarchies
Generalized Drinfeld-Sokolov (DS) hierarchies are constructed through local
reductions of Hamiltonian flows generated by monodromy invariants on the dual
of a loop algebra. Following earlier work of De Groot et al, reductions based
upon graded regular elements of arbitrary Heisenberg subalgebras are
considered. We show that, in the case of the nontwisted loop algebra
, graded regular elements exist only in those Heisenberg
subalgebras which correspond either to the partitions of into the sum of
equal numbers or to equal numbers plus one . We prove that the
reduction belonging to the grade regular elements in the case yields
the matrix version of the Gelfand-Dickey -KdV hierarchy,
generalizing the scalar case considered by DS. The methods of DS are
utilized throughout the analysis, but formulating the reduction entirely within
the Hamiltonian framework provided by the classical r-matrix approach leads to
some simplifications even for .Comment: 43 page
Noncommutative Spheres and Instantons
We report on some recent work on deformation of spaces, notably deformation
of spheres, describing two classes of examples. The first class of examples
consists of noncommutative manifolds associated with the so called
-deformations which were introduced out of a simple analysis in terms
of cycles in the -complex of cyclic homology. These examples have
non-trivial global features and can be endowed with a structure of
noncommutative manifolds, in terms of a spectral triple (\ca, \ch, D). In
particular, noncommutative spheres are isospectral
deformations of usual spherical geometries. For the corresponding spectral
triple (\cinf(S^{N}_\theta), \ch, D), both the Hilbert space of spinors \ch=
L^2(S^{N},\cs) and the Dirac operator are the usual ones on the
commutative -dimensional sphere and only the algebra and its action
on are deformed. The second class of examples is made of the so called
quantum spheres which are homogeneous spaces of quantum orthogonal
and quantum unitary groups. For these spheres, there is a complete description
of -theory, in terms of nontrivial self-adjoint idempotents (projections)
and unitaries, and of the -homology, in term of nontrivial Fredholm modules,
as well as of the corresponding Chern characters in cyclic homology and
cohomology.Comment: Minor changes, list of references expanded and updated. These notes
are based on invited lectures given at the ``International Workshop on
Quantum Field Theory and Noncommutative Geometry'', November 26-30 2002,
Tohoku University, Sendai, Japan. To be published in the workshop proceedings
by Springer-Verlag as Lecture Notes in Physic
On the Completeness of the Set of Classical W-Algebras Obtained from DS Reductions
We clarify the notion of the DS --- generalized Drinfeld-Sokolov ---
reduction approach to classical -algebras. We first strengthen an
earlier theorem which showed that an embedding can be associated to every DS reduction. We then use the fact that a
\W-algebra must have a quasi-primary basis to derive severe restrictions on
the possible reductions corresponding to a given embedding. In the
known DS reductions found to date, for which the \W-algebras are denoted by
-algebras and are called canonical, the
quasi-primary basis corresponds to the highest weights of the . Here we
find some examples of noncanonical DS reductions leading to \W-algebras which
are direct products of -algebras and `free field'
algebras with conformal weights . We also show
that if the conformal weights of the generators of a -algebra
obtained from DS reduction are nonnegative (which isComment: 48 pages, plain TeX, BONN-HE-93-14, DIAS-STP-93-0
Chiral de Rham complex on Riemannian manifolds and special holonomy
Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian
quantization of the supersymmetric non-linear sigma model, we suggest a setup
for the study of CDR on manifolds with special holonomy. We show how to
systematically construct global sections of CDR from differential forms, and
investigate the algebra of the sections corresponding to the covariantly
constant forms associated with the special holonomy. As a concrete example, we
construct two commuting copies of the Odake algebra (an extension of the N=2
superconformal algebra) on the space of global sections of CDR of a Calabi-Yau
threefold and conjecture similar results for G_2 manifolds. We also discuss
quasi-classical limits of these algebras.Comment: 49 pages, title changed, major rewrite with no changes in the main
theorems, published versio