1,747 research outputs found
Poisson Algebra of Wilson Loops and Derivations of Free Algebras
We describe a finite analogue of the Poisson algebra of Wilson loops in
Yang-Mills theory. It is shown that this algebra arises in an apparently
completely different context; as a Lie algebra of vector fields on a
non-commutative space. This suggests that non-commutative geometry plays a
fundamental role in the manifestly gauge invariant formulation of Yang-Mills
theory. We also construct the deformation of the loop algebra induced by
quantization, in the large N_c limit.Comment: 20 pages, no special macros necessar
Parton Model from Bi-local Solitonic Picture of the Baryon in two-dimensions
We study a previously introduced bi-local gauge invariant reformulation of
two dimensional QCD, called 2d HadronDynamics. The baryon arises as a
topological soliton in HadronDynamics. We derive an interacting parton model
from the soliton model, thus reconciling these two seemingly different points
of view. The valence quark model is obtained as a variational approximation to
HadronDynamics. A succession of better approximations to the soliton picture
are obtained. The next simplest case corresponds to a system of interacting
valence, `sea' and anti-quarks. We also obtain this `embellished' parton model
directly from the valence quark system through a unitary transformation. Using
the solitonic point of view, we estimate the quark and anti-quark distributions
of 2d QCD. Possible applications to Deep Inelastic Structure Functions are
pointed out.Comment: 12 page
Geometric Quantization and Two Dimensional QCD
In this article, we will discuss geometric quantization of 2d QCD with
fermionic and bosonic matter fields. We identify the respective large-N_c phase
spaces as the infinite dimensional Grassmannian and the infinite dimensional
Disc. The Hamiltonians are quadratic functions, and the resulting equations of
motion for these classical systems are nonlinear. In a previous publication,
the first author has shown that the linearization of the equations of motion
for the Grassmannian gave the `t Hooft equation. We will see that the
linearization in the bosonic case leads to the scalar analog of the `t Hooft
equation found by Tomaras.Comment: 46 pages, Latex, no figure
Poisson Algebra of Wilson Loops in Four-Dimensional Yang-Mills Theory
We formulate the canonical structure of Yang--Mills theory in terms of
Poisson brackets of gauge invariant observables analogous to Wilson loops. This
algebra is non--trivial and tractable in a light--cone formulation. For U(N)
gauge theories the result is a Lie algebra while for SU(N) gauge theories it is
a quadratic algebra. We also study the identities satsfied by the gauge
invariant observables. We suggest that the phase space of a Yang--Mills theory
is a co--adjoint orbit of our Poisson algebra; some partial results in this
direction are obtained.Comment: 32 Pages, 7 figures upon reques
A comment on generalized Schwinger effect
A spatially homogeneous, time-dependent, electric field can produce charged
particle pairs from the vacuum. When the electric field is constant, the mean
number of pairs which are produced depends on the electric field and the
coupling constant in a non-analytic manner, showing that this result cannot be
obtained from the standard perturbation theory of quantum electrodynamics. When
the electric field varies with time and vanishes asymptotically, the result may
depend on the coupling constant either analytically or non-analytically. We
investigate the nature of this dependence in detail. We show that the
dependence of particle production on coupling constant is non-analytic for a
class of time-dependent electric fields which vanish asymptotically when a
specific condition is satisfied. We also demonstrate that for another class of
electric fields, which vary rapidly, the dependence of particle production on
coupling constant is analytic.Comment: published versio
Symmetry Algebras of Large-N Matrix Models for Open Strings
We have discovered that the gauge invariant observables of matrix models
invariant under U() form a Lie algebra, in the planar large-N limit. These
models include Quantum Chromodynamics and the M(atrix)-Theory of strings. We
study here the gauge invariant states corresponding to open strings (`mesons').
We find that the algebra is an extension of a remarkable new Lie algebra by a product of more well-known algebras such as
and the Cuntz algebra. appears to be a generalization of
the Lie algebra of vector fields on the circle to non-commutative geometry. We
also use a representation of our Lie algebra to establish an isomorphism
between certain matrix models (those that preserve `gluon number') and open
quantum spin chains. Using known results on quantum spin chains, we are able to
identify some exactly solvable matrix models. Finally, the Hamiltonian of a
dimensionally reduced QCD model is expressed explicitly as an element of our
Lie algebra.Comment: 44 pages, 8 eps figures, 3 tables, LaTeX2.09; this is the published
versio
Multiparticle Schrodinger operators with point interactions in the plane
We study a system of N bosons in the plane interacting with delta function
potentials. After a coupling constant renormalization we show that the
Hamiltonian defines a self-adjoint operator and obtain a lower bound for the
energy. The same results hold if one includes a regular inter-particle
potential.Comment: 17 pages, Late
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