332 research outputs found
On the stability of Dirac sheet configurations
Using cooling for SU(2) lattice configurations, purely Abelian constant
magnetic field configurations were left over after the annihilation of
constituents that formed metastable Q=0 configurations. These so-called Dirac
sheet configurations were found to be stable if emerging from the confined
phase, close to the deconfinement phase transition, provided their Polyakov
loop was sufficiently non-trivial. Here we show how this is related to the
notion of marginal stability of the appropriate constant magnetic field
configurations. We find a perfect agreement between the analytic prediction for
the dependence of stability on the value of the Polyakov loop (the holonomy) in
a finite volume and the numerical results studied on a finite lattice in the
context of the Dirac sheet configurations
Quantum Arrival and Dwell Times via Idealised Clocks
A number of approaches to the problem of defining arrival and dwell time
probabilities in quantum theory make use of idealised models of clocks. An
interesting question is the extent to which the probabilities obtained in this
way are related to standard semiclassical results. In this paper we explore
this question using a reasonably general clock model, solved using path
integral methods. We find that in the weak coupling regime where the energy of
the clock is much less than the energy of the particle it is measuring, the
probability for the clock pointer can be expressed in terms of the probability
current in the case of arrival times, and the dwell time operator in the case
of dwell times, the expected semiclassical results. In the regime of strong
system-clock coupling, we find that the arrival time probability is
proportional to the kinetic energy density, consistent with an earlier model
involving a complex potential. We argue that, properly normalized, this may be
the generically expected result in this regime. We show that these conclusions
are largely independent of the form of the clock Hamiltonian.Comment: 19 pages, 4 figures. Published versio
Observables in Topological Yang-Mills Theories
Using topological Yang-Mills theory as example, we discuss the definition and
determination of observables in topological field theories (of Witten-type)
within the superspace formulation proposed by Horne. This approach to the
equivariant cohomology leads to a set of bi-descent equations involving the
BRST and supersymmetry operators as well as the exterior derivative. This
allows us to determine superspace expressions for all observables, and thereby
to recover the Donaldson-Witten polynomials when choosing a Wess-Zumino-type
gauge.Comment: 39 pages, Late
General bounds on the Wilson-Dirac operator
Lower bounds on the magnitude of the spectrum of the Hermitian Wilson-Dirac
operator H(m) have previously been derived for 0<m<2 when the lattice gauge
field satisfies a certain smoothness condition. In this paper lower bounds are
derived for 2p-2<m<2p for general p=1,2,...,d where d is the spacetime
dimension. The bounds can alternatively be viewed as localisation bounds on the
real spectrum of the usual Wilson-Dirac operator. They are needed for the
rigorous evaluation of the classical continuum limit of the axial anomaly and
index of the overlap Dirac operator at general values of m, and provide
information on the topological phase structure of overlap fermions. They are
also useful for understanding the instanton size-dependence of the real
spectrum of the Wilson-Dirac operator in an instanton background.Comment: 26 pages, 2 figures. v3: Completely rewritten with new material and
new title; to appear in Phys.Rev.
Towards Solving QCD in Light-Cone Quantization -- On the Spectrum of the Transverse Zero Modes for SU(2)
The formalism for a non-abelian pure gauge theory in (2+1) dimensions has
recently been derived within Discretized Light-Cone Quantization, restricting
to the lowest {\it transverse} momentum gluons. It is argued why this model can
be a paradigm for full QCD. The physical vacuum becomes non-trivial even in
light-cone quantization. The approach is brought here to tractable form by
suppressing by hand both the dynamical gauge and the constraint zero mode, and
by performing a Tamm-Dancoff type Fock-space truncation. Within that model the
Hamiltonian is diagonalized numerically, yielding mass spectra and
wavefunctions of the glue-ball states. We find that only color singlets have a
stable and discrete bound state spectrum. The connection with confinement is
discussed. The structure function of the gluons has a shape like . The existence of the continuum limit is verified by deriving a
coupled set of integral equations.Comment: 1 Latex file & 9 Postscript files; tarred, compressed and uuencode
Tube Model for Light-Front QCD
We propose the tube model as a first step in solving the bound state problem
in light-front QCD. In this approach we neglect transverse variations of the
fields, producing a model with 1+1 dimensional dynamics. We then solve the two,
three, and four particle sectors of the model for the case of pure glue SU(3).
We study convergence to the continuum limit and various properties of the
spectrum.Comment: 29 page
On Zero Modes and the Vacuum Problem -- A Study of Scalar Adjoint Matter in Two-Dimensional Yang-Mills Theory via Light-Cone Quantisation
SU(2) Yang-Mills Theory coupled to massive adjoint scalar matter is studied
in (1+1) dimensions using Discretised Light-Cone Quantisation. This theory can
be obtained from pure Yang-Mills in 2+1 dimensions via dimensional reduction.
On the light-cone, the vacuum structure of this theory is encoded in the
dynamical zero mode of a gluon and a constrained mode of the scalar field. The
latter satisfies a linear constraint, suggesting no nontrivial vacua in the
present paradigm for symmetry breaking on the light-cone. I develop a
diagrammatic method to solve the constraint equation. In the adiabatic
approximation I compute the quantum mechanical potential governing the
dynamical gauge mode. Due to a condensation of the lowest omentum modes of the
dynamical gluons, a centrifugal barrier is generated in the adiabatic
potential. In the present theory however, the barrier height appears too small
to make any impact in this odel. Although the theory is superrenormalisable on
naive powercounting grounds, the removal of ultraviolet divergences is
nontrivial when the constrained mode is taken into account. The open aspects of
this problem are discussed in detail.Comment: LaTeX file, 26 pages. 14 postscript figure
A Class of Exact Solutions of the Faddeev Model
A class of exact solutions of the Faddeev model, that is, the modified SO(3)
nonlinear sigma model with the Skyrme term, is obtained in the four dimensional
Minkowskian spacetime. The solutions are interpreted as the isothermal
coordinates of a Riemannian surface. One special solution of the static vortex
type is investigated numerically. It is also shown that the Faddeev model is
equivalent to the mesonic sector of the SU(2) Skyrme model where the baryon
number current vanishes.Comment: 20 pages, 7 figures, refs. adde
Tadpole-improved SU(2) lattice gauge theory
A comprehensive analysis of tadpole-improved SU(2) lattice gauge theory is
made. Simulations are done on isotropic and anisotropic lattices, with and
without improvement. Two tadpole renormalization schemes are employed, one
using average plaquettes, the other using mean links in Landau gauge.
Simulations are done with spatial lattice spacings in the range of about
0.1--0.4 fm. Results are presented for the static quark potential, the
renormalized lattice anisotropy (where is the ``temporal''
lattice spacing), and for the scalar and tensor glueball masses. Tadpole
improvement significantly reduces discretization errors in the static quark
potential and in the scalar glueball mass, and results in very little
renormalization of the bare anisotropy that is input to the action. We also
find that tadpole improvement using mean links in Landau gauge results in
smaller discretization errors in the scalar glueball mass (as well as in the
static quark potential), compared to when average plaquettes are used. The
possibility is also raised that further improvement in the scalar glueball mass
may result when the coefficients of the operators which correct for
discretization errors in the action are computed beyond tree level.Comment: 14 pages, 7 figures (minor changes to overall scales in Fig.1; typos
removed from Eqs. (3),(4),(15); some rewording of Introduction
Quark zero modes in intersecting center vortex gauge fields
The zero modes of the Dirac operator in the background of center vortex gauge
field configurations in and are examined. If the net flux in D=2
is larger than 1 we obtain normalizable zero modes which are mainly localized
at the vortices. In D=4 quasi-normalizable zero modes exist for intersecting
flat vortex sheets with the Pontryagin index equal to 2. These zero modes are
mainly localized at the vortex intersection points, which carry a topological
charge of . To circumvent the problem of normalizability the
space-time manifold is chosen to be the (compact) torus \T^2 and \T^4,
respectively. According to the index theorem there are normalizable zero modes
on \T^2 if the net flux is non-zero. These zero modes are localized at the
vortices. On \T^4 zero modes exist for a non-vanishing Pontryagin index. As
in these zero modes are localized at the vortex intersection points.Comment: 20 pages, 4 figures, LaTeX2e, references added, treatment of ideal
vortices on the torus shortene
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