105 research outputs found
Variational Wave Functionals in Quantum Field Theory
Variational (Rayleigh-Ritz) methods are applied to local quantum field theory. For scalar theories the wave functional is parametrized in the form of a superposition of Gaussians and the expectation value of the Hamiltonian is expressed in a form that can be minimized numerically. A scheme of successive refinements of the superposition is proposed that may converge to the exact functional. As an illustration, a simple numerical approximation for the effective potential is worked out based on minimization with respect to five variational parameters. A variational principle is formulated for the fermion vacuum energy as a functional of the scalar fields to which the fermions are coupled. The discussion in this paper is given for scalar and fermion interactions in 1+1 dimensions. The extension to higher dimensions encounters a more involved structure of ultraviolet divergences and is deferred to future work
Interquark Potential in Schrodinger Representation
Static charges are introduced in Yang-Mills theory via coupling to heavy
fermions. The states containing static color charges are constructed using
integration over gauge transformations. A functional representation for
interquark potential is obtained. This representation provides a simple
criterion for confinement.Comment: 9pp., Late
Electromagnetic fields of a massless particle and the eikonal
Electromagnetic fields of a massless charged particle are described by a
gauge potential that is almost everywhere pure gauge. Solution of quantum
mechanical wave equations in the presence of such fields is therefore immediate
and leads to a new derivation of the quantum electrodynamical eikonal
approximation. The elctromagnetic action in the eikonal limit is localised on a
contour in a two-dimensional Minkowski subspace of four-dimensional space-time.
The exact S-matrix of this reduced theory coincides with the eikonal
approximation, and represents the generalisatin to electrodynamics of the
approach of 't Hooft and the Verlinde's to Planckian scattering.Comment: The missing overdot -- signifying the differentiation
in eqs. (23) and (24) -- is
inserted. Also, obsolete macro has been fixed. Plain TeX, 13 page
Low-dimensional long-range topological structure in the QCD vacuum
Lattice topological charge associated with Ginsparg-Wilson fermions exhibits
generic topological stability over quantum ensemble of configurations
contributing to the QCD path integral. Moreover, the underlying chiral symmetry
leads to the suppression of ultraviolet noise in the associated topological
charge densities ("chiral smoothing"). This provides a solid foundation for the
direct study of the role of topological charge fluctuations in the physics of
QCD vacuum. Using these tools it was recently demonstrated that: (a) there is a
well-defined space-time structure (order) in topological charge density
(defined through overlap fermions) for typical configurations contributing to
QCD path integral; (b) this fundamental structure is low-dimensional,
exhibiting sign-coherent behavior on subsets of dimension less than four and
not less than one; (c) the structure has a long-range global character
(spreading over maximal space-time distances) and is built around the locally
one-dimensional network of strong fields (skeleton). In this talk we elaborate
on certain aspects and implications of these results.Comment: 3 pages, 1 figure; Lattice2003(topology
Center Vortices, Nexuses, and Fractional Topological Charge
It has been remarked in several previous works that the combination of center
vortices and nexuses (a nexus is a monopole-like soliton whose world line
mediates certain allowed changes of field strengths on vortex surfaces) carry
topological charge quantized in units of 1/N for gauge group SU(N). These
fractional charges arise from the interpretation of the standard topological
charge integral as a sum of (integral) intersection numbers weighted by certain
(fractional) traces. We show that without nexuses the sum of intersection
numbers gives vanishing topological charge (since vortex surfaces are closed
and compact). With nexuses living as world lines on vortices, the contributions
to the total intersection number are weighted by different trace factors, and
yield a picture of the total topological charge as a linking of a closed nexus
world line with a vortex surface; this linking gives rise to a non-vanishing
but integral topological charge. This reflects the standard 2\pi periodicity of
the theta angle. We argue that the Witten-Veneziano relation, naively violating
2\pi periodicity, scales properly with N at large N without requiring 2\pi N
periodicity. This reflects the underlying composition of localized fractional
topological charge, which are in general widely separated. Some simple models
are given of this behavior. Nexuses lead to non-standard vortex surfaces for
all SU(N) and to surfaces which are not manifolds for N>2. We generalize
previously-introduced nexuses to all SU(N) in terms of a set of fundamental
nexuses, which can be distorted into a configuration resembling the 't
Hooft-Polyakov monopole with no strings. The existence of localized but
widely-separated fractional topological charges, adding to integers only on
long distance scales, has implications for chiral symmetry breakdown.Comment: 15 pages, revtex, 6 .eps figure
D-Branes and their Absorptivity in Born-Infeld Theory
Standard methods of nonlinear dynamics are used to investigate the stability
of particles, branes and D-branes of abelian Born-Infeld theory. In particular
the equation of small fluctuations about the D-brane is derived and converted
into a modified Mathieu equation and - complementing earlier low-energy
investigations in the case of the dilaton-axion system - studied in the
high-energy domain. Explicit expressions are derived for the S-matrix and
absorption and reflection amplitudes of the scalar fluctuation in the presence
of the D-brane. The results confirm physical expectations and numerical studies
of others. With the derivation and use of the (hitherto practically unknown)
high energy expansion of the Floquet exponent our considerations also close a
gap in earlier treatments of the Mathieu equation.Comment: latex, 26 pages, 4 figures, one reference added, to appear in Nucl.
Phys.
Variational Principle in the Algebra of Asymptotic Fields
This paper proposes a variational principle for the solutions of quantum
field theories in which the ``trial functions'' are chosen from the algebra of
asymptotic fields, and illustrates this variational principle in simple cases.Comment: 15 pages, Latex, no figure
Low-Dimensional Long-Range Topological Charge Structure in the QCD Vacuum
While sign-coherent 4-dimensional structures cannot dominate topological
charge fluctuations in the QCD vacuum at all scales due to reflection
positivity, it is possible that enhanced coherence exists over extended
space-time regions of lower dimension. Using the overlap Dirac operator to
calculate topological charge density, we present evidence for such structure in
pure-glue SU(3) lattice gauge theory. It is found that a typical equilibrium
configuration is dominated by two oppositely-charged sign-coherent connected
structures (``sheets'') covering about 80% of space-time. Each sheet is built
from elementary 3-d cubes connected through 2-d faces, and approximates a
low-dimensional curved manifold (or possibly a fractal structure) embedded in
the 4-d space. At the heart of the sheet is a ``skeleton'' formed by about 18%
of the most intense space-time points organized into a global long-range
structure, involving connected parts spreading over maximal possible distances.
We find that the skeleton is locally 1-dimensional and propose that its
geometrical properties might be relevant for understanding the possible role of
topological charge fluctuations in the physics of chiral symmetry breaking.Comment: 4 pages RevTeX, 4 figures; v2: 6 pages, 5 figures, more explanations
provided, figure and references added, published versio
Cut Diagrams for High Energy Scatterings
A new approach is introduced to study QCD amplitudes at high energy and
comparatively small momentum transfer. Novel cut diagrams, representing
resummation of Feynman diagrams, are used to simplify calculation and to avoid
delicate cancellations encountered in the usual approach. Explicit calculation
to the 6th order is carried out to demonstrate the advantage of cut diagrams
over Feynman diagrams.Comment: uu-encoded file containing a latex manuscript with 14 postscript
figure
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