21 research outputs found
Non-Abelian Stokes Theorem and Quark Confinement in SU(3) Yang-Mills Gauge Theory
We derive a new version of SU(3) non-Abelian Stokes theorem by making use of
the coherent state representation on the coset space , the flag space. Then we outline a derivation of the area law of the
Wilson loop in SU(3) Yang-Mills theory in the maximal Abelian gauge (The
detailed exposition will be given in a forthcoming article). This derivation is
performed by combining the non-Abelian Stokes theorem with the reformulation of
the Yang-Mills theory as a perturbative deformation of a topological field
theory recently proposed by one of the authors. Within this framework, we show
that the fundamental quark is confined even if is broken by partial
gauge fixing into just as is broken to . An
origin of the area law is related to the geometric phase of the Wilczek-Zee
holonomy for U(2). Abelian dominance is an immediate byproduct of these results
and magnetic monopole plays the dominant role in this derivation.Comment: 14 pages, Latex, no figures, version accepted for publication in Mod.
Phys. Lett. A (some comments are added in the final parts
Flavor-Dependence and Higher Orders of Gauge-Independent Solutions in Strong Coupling Gauge Theory
The fermion flavor dependence of non-perturbative solutions in the
strong coupling phase of the gauge theory is reexamined based on the
interrelation between the inversion method and the Schwinger-Dyson equation
approach. Especially we point out that the apparent discrepancy on the value of
the critical coupling in QED will be resolved by taking into account the higher
order corrections which inevitably lead to the flavor-dependence. In the
quenched QED, we conclude that the gauge-independent critical point
obtained by the inversion method to the lowest order will be
reduced to the result of the Schwinger-Dyson equation in the
infinite order limit, but its convergence is quite slow. This is shown by
adding the chiral-invariant four-fermion interaction.Comment: CHIBA-EP-72, 13 pages (including 1 Table), LaTex fil
The exact decomposition of gauge variables in lattice Yang-Mills theory
In this paper, we consider lattice versions of the decomposition of the Yang-
Mills field a la Cho-Faddeev-Niemi, which was extended by Kondo, Shinohara and
Murakami in the continuum formulation. For the SU(N) gauge group, we propose a
set of defining equations for specifying the decomposition of the gauge link
variable and solve them exactly without using the ansatz adopted in the
previous studies for SU(2) and SU(3). As a result, we obtain the general form
of the decomposition for SU(N) gauge link variables and confirm the previous
results obtained for SU(2) and SU(3).Comment: 16 page
Abelian-Projected Effective Gauge Theory of QCD with Asymptotic Freedom and Quark Confinement
We give an outline of a recent proof that the low-energy effective gauge
theory exhibiting quark confinement due to magnetic monopole condensation can
be derived from QCD without any specific assumption. We emphasize that the
low-energy effective abelian gauge theories obtained here give the dual
description of the same physics in the low-energy region. They show that the
QCD vacuum is nothing but the dual (type II) superconductor.Comment: 15 pages, Latex, no figures, Talk given at YKIS'97, Non-perturbative
QCD, Kyot
Abelian-Projected Effective Gauge Theory of QCD with Asymptotic Freedom and Quark Confinement
Starting from SU(2) Yang-Mills theory in 3+1 dimensions, we prove that the
abelian-projected effective gauge theories are written in terms of the maximal
abelian gauge field and the dual abelian gauge field interacting with monopole
current. This is performed by integrating out all the remaining non-Abelian
gauge field belonging to SU(2)/U(1). We show that the resulting abelian gauge
theory recovers exactly the same one-loop beta function as the original
Yang-Mills theory. Moreover, the dual abelian gauge field becomes massive if
the monopole condensation occurs. This result supports the dual superconductor
scenario for quark confinement in QCD. We give a criterion of dual
superconductivity and point out that the monopole condensation can be estimated
from the classical instanton configuration. Therefore there can exist the
effective abelian gauge theory which shows both asymptotic freedom and quark
confinement based on the dual Meissner mechanism. Inclusion of arbitrary number
of fermion flavors is straightforward in this approach. Some implications to
lower dimensional case will also be discussed.Comment: 39 pages, Latex, no figures, (2.2, 4.1, 4.3 are modified; 4.4,
Appendices A,B,C and references are added. No change in conclusion
Preheating of the nonminimally coupled inflaton field
We investigate preheating of an inflaton field coupled nonminimally to
a spacetime curvature. In the case of a self-coupling inflaton potential
, the dynamics of preheating changes by the effect of
the negative . We find that the nonminimal coupling works in two ways.
First, since the initial value of inflaton field for reheating becomes
smaller with the increase of , the evolution of the inflaton quanta is
delayed for fixed . Second, the oscillation of the inflaton field is
modified and the nonadiabatic change around occurs significantly. That
makes the resonant band of the fluctuation field wider. Especially for strong
coupling regimes , the growth of the inflaton flutuation is
dominated by the resonance due to the nonminimal coupling, which leads to the
significant enhancement of low momentum modes. Although the final variance of
the inflaton fluctuation does notchange significantly compared with the
minimally coupled case, we have found that the energy transfer from the
homogeneous inflaton to created particles efficiently occurs for .Comment: 13pages, 11figure
Infrared and ultraviolet asymptotic solutions to gluon and ghost propagators in Yang-Mills theory
We examine the possibility that there may exist a logarithmic correction to
the infrared asymptotic solution with power behavior which has recently been
found for the gluon and Faddeev-Popov ghost propagators in the Landau gauge. We
propose a new Ansatz to find a pair of solutions for the gluon and ghost form
factors by solving the coupled Schwinger-Dyson equation under a simple
truncation. This Ansatz enables us to derive the infrared and ultraviolet
asymptotic solutions simultaneously and to understand why the power solution
and the logarithmic solution is possible only in the infrared and ultraviolet
limit respectively. Even in the presence of the logarithmic correction, the
gluon propagator vanishes and the ghost propagator is enhanced in the infrared
limit, and the gluon-ghost-antighost coupling constant has an infrared fixed
point (but with a different function). This situation is consistent
with Gribov-Zwanziger confinement scenario and color confinement criterion of
Kugo and Ojima.Comment: 15 pages, 2 figures, version to appear in Phys. Lett.