87 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
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
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
Rigorous QCD-Potential for the -System at Threshold
Recent evidence for the top mass in the region of 160 for the first
time provides an opportunity to use the full power of relativistic quantum
field theoretical methods, available also for weakly bound systems. Because of
the large decay width \G of the top quark individual energy-levels in
"toponium" will be unobservable. However, the potential for the
system, based on a systematic expansion in powers of the strong coupling
constant \a_s can be rigorously derived from QCD and plays a central role in
the threshold region. It is essential that the neglect of nonperturbative
(confining) effects is fully justified here for the first time to a large
accuracy, also just {\it because} of the large \G. The different
contributions to that potential are computed from real level corrections near
the bound state poles of the -system which for \G \ne 0 move into
the unphysical sheet of the complex energy plane. Thus, in order to obtain the
different contributions to that potential we may use the level corrections at
that (complex) pole. Within the relevant level shifts we especially emphasize
the corrections of order O(\a_s^4 m_t) and numerically comparable ones to
that order also from electroweak interactions which may become important as
well.Comment: 36 pages (mailer uncorrupted version), TUW-94-1
Calculable observables in quantum chromodynamics I
A simple heuristic proof of infrared finiteness to all orders of perturbation theory is given for a class of observables in massless field theories including quantum chromodynamics. This class includes the average energy E( Omega ) carried into a given solid angular region Omega by final-state particles in e/sup +/e/sup -/ annihilation and its positive integral powers; it also includes energy correlations between different angular regions: E( Omega /sub 1/)E( Omega /sub 2/) ... E( Omega /sub N/). It is argued that appropriately defined inclusive jet cross sections are infrared finite, even for vanishing fractional energy resolutions. Extensions to lepton-hadron and hadron- hadron collisions are described. (8 refs)
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